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Turkish Journal of Analysis and Number Theory

ISSN (Print): 2333-1100

ISSN (Online): 2333-1232

Website: http://www.sciepub.com/journal/TJANT

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Article

Hermite-Hadamard Type Inequalities for s-Convex Stochastic Processes in the Second Sense

1Department of Mathematics, Faculty of Science and Arts, Ordu University, Ordu, Turkey


Turkish Journal of Analysis and Number Theory. 2014, 2(6), 202-207
DOI: 10.12691/tjant-2-6-3
Copyright © 2014 Science and Education Publishing

Cite this paper:
ERHAN SET, MUHARREM TOMAR, SELAHATTIN MADEN. Hermite-Hadamard Type Inequalities for s-Convex Stochastic Processes in the Second Sense. Turkish Journal of Analysis and Number Theory. 2014; 2(6):202-207. doi: 10.12691/tjant-2-6-3.

Correspondence to: MUHARREM  TOMAR, Department of Mathematics, Faculty of Science and Arts, Ordu University, Ordu, Turkey. Email: muharremtomar@odu.edu.tr

Abstract

In this study, s-convex stochastic processes in the second sense are presented and some well-known results concerning s-convex functions are extended to s-convex stochastic processes in the second sense. Also, we investigate relation between s-convex stochastic processes in the second sense and convex stochastic processes.

Keywords

References

[1]  K. Nikodem, on convex stochastic processes, Aequationes Mathematicae 20 (1980) 184-197.
 
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[8]  D. Kotrys, Hermite-hadamart inequality for convex stochastic processes, Aequationes Mathematicae 83 (2012) 143-151.
 
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Article

Birth of Compound Numbers

1Department of Computer Science, Jamia Hamdard University, Hamdard Nagar, New Delhi, INDIA


Turkish Journal of Analysis and Number Theory. 2014, 2(6), 208-219
DOI: 10.12691/tjant-2-6-4
Copyright © 2014 Science and Education Publishing

Cite this paper:
Ranjit Biswas. Birth of Compound Numbers. Turkish Journal of Analysis and Number Theory. 2014; 2(6):208-219. doi: 10.12691/tjant-2-6-4.

Correspondence to: Ranjit  Biswas, Department of Computer Science, Jamia Hamdard University, Hamdard Nagar, New Delhi, INDIA. Email: ranjitbiswas@yahoo.com

Abstract

In this paper the author introduces a new kind of numbers called by ‘Compound Numbers’. A region R may or may not have imaginary object. A region even may have more than one imaginary objects too. Corresponding to an imaginary object (if exists) of a region R, we get compound objects for the region R. Imaginary objects and compound objects of a region R are not members of R and so they are called imaginary with respect to the region R only (i.e. it is a local characteristics property with respect to the region concerned), as they could be core members of another region. Every region has its own set of imaginary numbers (if exist). As a particular instance, the compound objects of the set of real numbers are the complex numbers (of existing concept). In this paper the author discovers imaginary objects of the region C (the set of complex numbers). The compound objects of C are called by ‘compound numbers’. Collection of all compound numbers is denoted by the set E. This work just reports the birth of compound numbers, not further details at this stage. It is claimed that “Theory of Numbers” will get a new direction by the birth of compound numbers. A new “Theory of Objects’ and the classical “Theory of Numbers” as a special case of it were also studied in . In this paper we say that every complete region has its own ‘Theory of Numbers’, where the classical ‘theory of numbers’ is just a special instance corresponding to a particular complete region RR. Consequently, we also introduce a new field called by “Object Geometry” of a complete region, being a generalization of our classical geometry of the existing style, from elementary to the higher level.

Keywords

References

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Article

Note on a Partition Function Which Assumes All Integral Values

1Department of Mathematics, Goa University, Taleigao Plateau, Goa, India


Turkish Journal of Analysis and Number Theory. 2014, 2(6), 220-222
DOI: 10.12691/tjant-2-6-5
Copyright © 2014 Science and Education Publishing

Cite this paper:
Manvendra Tamba. Note on a Partition Function Which Assumes All Integral Values. Turkish Journal of Analysis and Number Theory. 2014; 2(6):220-222. doi: 10.12691/tjant-2-6-5.

Correspondence to: Manvendra  Tamba, Department of Mathematics, Goa University, Taleigao Plateau, Goa, India. Email: tamba@unigoa.ac.in

Abstract

Let G(n) denote the number of partitions of n into distinct parts which are of the form 2m, 3m, 5m, 6m-3, 8m-3, 9m-3 or 11m-3 with parts of the form 2m, 3m, 6m-3, or 11m-3 being even in number minus the number of them with parts of the form 2m, 3m, 6m-3, or 11m-3 being odd in number. In this paper, we prove that G(n) assumes all integral values and does so infinitely often.

Keywords

References

[1]  G.E. Andrews, The Theory of Partitions, (G.-C. Rota, Ed.), Encyclopedia of Math. And its Applications, Vol. 2, Addison-Wesley, Reading, MA, 1976.
 
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[4]  J. Lovejoy, Lacunary Partition Functions, Math. Research Letters, 9 (2002) 191-198.
 
[5]  M.Tamba, On a partition function which assumes all integral values, J.Number Theory 41 (1992) 77-86.
 

Article

A Double Inequality for the Harmonic Number in Terms of the Hyperbolic Cosine

1College of Information and Business, Zhongyuan University of Technology, Zhengzhou City, Henan Province, China

2College of Mathematics, Inner Mongolia University for Nationalities, Tongliao City, Inner Mongolia Autonomous Region, China

3Department of Mathematics, College of Science, Tianjin Polytechnic University, Tianjin City, China;Institute of Mathematics, Henan Polytechnic University, Jiaozuo City, Henan Province, China


Turkish Journal of Analysis and Number Theory. 2014, 2(6), 223-225
DOI: 10.12691/tjant-2-6-6
Copyright © 2014 Science and Education Publishing

Cite this paper:
Da-Wei Niu, Yue-Jin Zhang, Feng Qi. A Double Inequality for the Harmonic Number in Terms of the Hyperbolic Cosine. Turkish Journal of Analysis and Number Theory. 2014; 2(6):223-225. doi: 10.12691/tjant-2-6-6.

Correspondence to: Da-Wei  Niu, College of Information and Business, Zhongyuan University of Technology, Zhengzhou City, Henan Province, China. Email: nnddww@163.com

Abstract

In the paper, the author present an inequality for bounding the harmonic number in terms of the hyperbolic cosine.

Keywords

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Article

Generalized Inequalities Related to the Classical Euler’s Gamma Function

1Department of Mathematics, University for Development Studies, Navrongo Campus, Navrongo UE/R, Ghana


Turkish Journal of Analysis and Number Theory. 2014, 2(6), 226-229
DOI: 10.12691/tjant-2-6-7
Copyright © 2014 Science and Education Publishing

Cite this paper:
Kwara Nantomah. Generalized Inequalities Related to the Classical Euler’s Gamma Function. Turkish Journal of Analysis and Number Theory. 2014; 2(6):226-229. doi: 10.12691/tjant-2-6-7.

Correspondence to: Kwara  Nantomah, Department of Mathematics, University for Development Studies, Navrongo Campus, Navrongo UE/R, Ghana. Email: mykwarasoft@yahoo.com, knantomah@uds.edu.gh

Abstract

This paper presents some inequalities concerning certain ratios of the classical Euler’s Gamma function. The results generalized some recent results.

Keywords

References

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[3]  F. Merovci, Power Product Inequalities for the Γk Function, Int. Journal of Math. Analysis, 4(21)(2010), 1007-1012.
 
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Article

On the Error Term for the Number of Integral Ideals in Galois Extensions

1School of Mathematics, Hefei University of Technology, Hefei, China


Turkish Journal of Analysis and Number Theory. 2014, 2(6), 230-232
DOI: 10.12691/tjant-2-6-8
Copyright © 2014 Science and Education Publishing

Cite this paper:
Sanying Shi. On the Error Term for the Number of Integral Ideals in Galois Extensions. Turkish Journal of Analysis and Number Theory. 2014; 2(6):230-232. doi: 10.12691/tjant-2-6-8.

Correspondence to: Sanying  Shi, School of Mathematics, Hefei University of Technology, Hefei, China. Email: vera123_99@hotmail.com

Abstract

Suppose that E is an algebraic number field over the rational field Let a(n) be the number of integral ideals in E with norm n and Δ(x) denote the remainder term in the asymptotic formula of the l-th integral power sum of a(n). In this paper the bound of the average behavior of Δ(x) is given. This result constitutes an improvement upon that of Lü and Wang for the error terms in mean value.

Keywords

References

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Article

Generalized Fibonacci – Like Sequence Associated with Fibonacci and Lucas Sequences

1Schools of Studies in Mathematics, Vikram University Ujjain, (M. P.) India

2Department of Mathematical Sciences and Computer application, Bundelkhand University, Jhansi (U. P.)

3Department of Mathematics, Mandsaur Institute of Technology, Mandsaur (M. P.) India


Turkish Journal of Analysis and Number Theory. 2014, 2(6), 233-238
DOI: 10.12691/tjant-2-6-9
Copyright © 2014 Science and Education Publishing

Cite this paper:
Yogesh Kumar Gupta, Mamta Singh, Omprakash Sikhwal. Generalized Fibonacci – Like Sequence Associated with Fibonacci and Lucas Sequences. Turkish Journal of Analysis and Number Theory. 2014; 2(6):233-238. doi: 10.12691/tjant-2-6-9.

Correspondence to: Yogesh  Kumar Gupta, Schools of Studies in Mathematics, Vikram University Ujjain, (M. P.) India. Email: yogeshgupta.880@rediffmail.com

Abstract

The Fibonacci sequence, Lucas numbers and their generalization have many interesting properties and applications to almost every field. Fibonacci sequence is defined by the recurrence formula Fn=Fn-1+Fn-2, , and F0=0, F1=1, where Fn is a nth number of sequence. Many authors have been defined Fibonacci pattern based sequences which are popularized and known as Fibonacci-Like sequences. In this paper, Generalized Fibonacci-Like sequence is introduced and defined by the recurrence relation Bn=Bn-1+Bn-2, with B0=2s, B1=s+1, where s being a fixed integers. Some identities of Generalized Fibonacci-Like sequence associated with Fibonacci and Lucas sequences are presented by Binet’s formula. Also some determinant identities are discussed.

Keywords

References

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[5]  B. Singh, Omprakash Sikhwal, and Yogesh Kumar Gupta, “Generalized Fibonacci-Lucas Sequence, Turkish Journal of Analysis and Number Theory, Vol.2, No.6. (2014), 193-197.
 
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[10]  M. Singh, Y. Gupta, O. Sikhwal, Generalized Fibonacci-Lucas Sequences its Properties, Global Journal of Mathematical Analysis, 2 (3) 2014, 160-168.
 
[11]  M. Singh, Y. Gupta, O. Sikhwal, “Identities of Generalized Fibonacci-Like Sequence.” Turkish Journal of Analysis and Number Theory, vol.2, no. 5 (2014): 170-175. doi:10.12691/tjant 2-5-3.
 
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Article

An Application of Generalized Bessel Functions on Certain Subclasses of Analytic Functions

1School of Advanced Sciences, VIT University Vellore - 632014, Tamilnadu, India


Turkish Journal of Analysis and Number Theory. 2015, 3(1), 1-6
DOI: 10.12691/tjant-3-1-1
Copyright © 2015 Science and Education Publishing

Cite this paper:
G. Murugusundaramoorthy, T. Janani. An Application of Generalized Bessel Functions on Certain Subclasses of Analytic Functions. Turkish Journal of Analysis and Number Theory. 2015; 3(1):1-6. doi: 10.12691/tjant-3-1-1.

Correspondence to: G.  Murugusundaramoorthy, School of Advanced Sciences, VIT University Vellore - 632014, Tamilnadu, India. Email: gmsmoorthy@yahoo.com

Abstract

The purpose of the present paper is to investigate some characterization for generalized Bessel functions of first kind to be in the new subclasses of β uniformly starlike and β uniformly convex functions of order α. Further we point out consequences of our main results.

Keywords

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Article

Common Fixed Point Results for Generalized Symmetric Meir-Keeler Contraction

1Department of Mathematics Govt. P. G. Arts & Science College Ratlam (M. P.) India


Turkish Journal of Analysis and Number Theory. 2015, 3(1), 7-11
DOI: 10.12691/tjant-3-1-2
Copyright © 2015 Science and Education Publishing

Cite this paper:
Bhavana Deshpande, Amrish Handa. Common Fixed Point Results for Generalized Symmetric Meir-Keeler Contraction. Turkish Journal of Analysis and Number Theory. 2015; 3(1):7-11. doi: 10.12691/tjant-3-1-2.

Correspondence to: Bhavana  Deshpande, Department of Mathematics Govt. P. G. Arts & Science College Ratlam (M. P.) India. Email: bhavnadeshpande@yahoo.com

Abstract

We introduce the concept of generalized weakly compatibility for the pair {F,G} of mappings F,G:X×X→X and also introduce the concept of common fixed point of the mappings F,G:X×X→X. We establish a common fixed point theorem for generalized weakly compatible pair of mappings F,G:X×X→X without mixed monotone property of any mapping under generalized symmetric Meir-Keeler contraction on a non complete metric space, which is not partially ordered. An example supporting to our result has also been cited. We improve, extend and generalize several known results.

Keywords

References

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[6]  B. Deshpande and A. Handa, Application of coupled fixed point technique in solving integral equations on modified intuitionistic fuzzy metric spaces, Adv. Fuzzy Syst. Volume 2014, Article ID 348069, 11 pages. 10
 
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Article

On the Numerical Regularity in the aspect of Prime Numbers

1Mathematical Society, Foundation Public School, Karachi, Pakistan


Turkish Journal of Analysis and Number Theory. 2015, 3(1), 12-16
DOI: 10.12691/tjant-3-1-3
Copyright © 2015 Science and Education Publishing

Cite this paper:
Shaad P. Sufi. On the Numerical Regularity in the aspect of Prime Numbers. Turkish Journal of Analysis and Number Theory. 2015; 3(1):12-16. doi: 10.12691/tjant-3-1-3.

Correspondence to: Shaad  P. Sufi, Mathematical Society, Foundation Public School, Karachi, Pakistan. Email: shaadpyarali@gmail.com

Abstract

The purpose of this paper is to introduce a new pattern in Primes numbers, to eliminate the randomness in their patterns. This paper also justifies the solutions in a numerical and geometric manner. The Prime Function provides further distinction in the nature of Prime Numbers by distinguishing the nature of normality and Abnormality in Prime Numbers. To verify the normality of corresponding Prime numbers, the Sufi primality test is formed. Also using the Prime Function, the formula for the approximate sum of Prime Numbers is derived. The limitations and conditions of the Prime function are also stated. These factors provide a panoramic view of the Prime Function and its potential factor in Number Theory .

Keywords

References

[1]  https://www.maa.org/sites/default/files/pdf/upload_library/22/Ford /Granville.pdf.
 
[2]  http://annals.math.princeton.edu/2014/179-3/p07.
 
[3]  http://en.wikipedia.org/wiki/Lucas_primality_test.