Welcome to Turkish Journal of Analysis and Number Theory

Turkish Journal of Analysis and Number Theory is a peer reviewed, open access journal that devotes exclusively to the publication of high quality research and review papers in the fields of number theory and analysis. An importance is placed on a vital and important developments in number theory, analytic number theory, p-adic analysis, q-analysis with its applications, fractional calculus, functional analysis, asymptotic analysis, differential geometry, theory of mathematical inequalities, topology, geometric analysis, numerical verification method, mathematical physics, semigroup theory, relativistic quantum mechanics, summability theory, sequences and series in functional analysis, line theory, general algebra, applied mathematics, complex analysis, stochastic control and stochastic stability, matrix transformations, normed structures, fuzzy set theory, enumerative and analytic combinatorics. Turkish Journal of Analysis and Number Theory is published in partnership with Hasan Kalyoncu University.

ISSN (Print): 2333-1100

ISSN (Online): 2333-1232

Editor-in-Chief: Mehmet Acikgoz, Feng Qi, Cenap Özel

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

   

Article

On New Weighted Ostrowski Type inequalities Involving Integral Means over End Intervals and Application

1Department of Fundamental and Applied Sciences, Universiti Teknologi Petronas, Malaysia

2Department of Mathematics, University of Hail, 2440, Saudi Arabia


Turkish Journal of Analysis and Number Theory. 2015, 3(2), 61-67
doi: 10.12691/tjant-3-2-5
Copyright © 2015 Science and Education Publishing

Cite this paper:
A. Qayyum, M. Shoaib, I. Faye. On New Weighted Ostrowski Type inequalities Involving Integral Means over End Intervals and Application. Turkish Journal of Analysis and Number Theory. 2015; 3(2):61-67. doi: 10.12691/tjant-3-2-5.

Correspondence to: I.  Faye, Department of Fundamental and Applied Sciences, Universiti Teknologi Petronas, Malaysia. Email: ibrahima_faye@petronas.com.my

Abstract

The aim of this paper is to establish new inequalities using weight function which generalizes the inequalities of Dragomir, Wang and Cerone. In this article we obtain bounds for the deviation of a function from a combination of weighted integral means over the end intervals covering the entire interval. A variety of earlier results are recaptured as particular instances of the current development. Applications for cumulative distribution function is also discussed.

Keywords

References

[1]  P. Cerone, A new Ostrowski type inequality involving integral Means over end intervals, Tamkang Journal Of Mathematics Volume 33, Number 2, 2002.
 
[2]  P. Cerone and S.S. Dragomir, Trapezoidal type rules from an inequalities point of view, Handbook of Analytic-Computational Methods in Applied Mathematics, CRC Press N.Y. (2000).
 
[3]  X. L. Cheng, Improvement of some Ostrowski-Grüss type inequalities, Comput. Math. Appl. 42 (2001), 109 114.
 
[4]  S. S. Dragomir and N. S. Barnett, An Ostrowski type inequality for mappings whose second derivatives are bounded and applications, RGMIA Research Report Collection, V.U.T., 1(1999), 67-76.
 
[5]  S. S. Dragomir and S. Wang, A new inequality Ostrowski’s type in Lp-norm, Indian J. of Math. 40 (1998), 299-304.
 
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[6]  S. S. Dragomir and S. Wang, A new inequality Ostrowski’s type in L1-norm and applications to some special means and some numerical quadrature rules, Tamkang J. of Math. 28(1997), 239-244.
 
[7]  S. S. Dragomir and S. Wang, An inequality Ostrowski-Grüss type and its applications to the estimation of error bounds for some special means and for some numerical quadrature rules, Computers Math. Applic. 33(1997), 15-22.
 
[8]  S. S. Dragomir and S. Wang, Applications of Ostrowski’s inequality to the estimation of error bounds for some special means and to some numerical quadrature rules, Appl. Math.Lett. 11(1998), 105-109.
 
[9]  S. S. Dragomir and S. Wang, An inequality of Ostrowski-Grüs type and its applications to the estimation of error bounds for some special means and for some numerical quadrature rules, Comput. Math. Appl., 33 (11), 15-20, (1997).
 
[10]  Z. Liu, Some companions of an Ostrowski type inequality and application, J. Inequal. in Pure and Appl. Math, 10(2), 2009, Art. 52.
 
[11]  G. V. Milovanovicˊ and J. E. Pecaricˊ, On generalization of the inequality of A. Ostrowski and some related applications, Univ. Beograd Publ. Elektrotehn. Fak. Ser. Mat. Fiz. (544-576), 155-158, (1976).
 
[12]  D. S. Mitrinovicˊ, J. E. Pecaricˊ and A. M. Fink, Inequalities for Functions and Their Integrals and Derivatives, Kluwer Academic Publishers, 1994.
 
[13]  A.Ostrowski, Uber die Absolutabweichung einer di erentienbaren Funktionen von ihren Integralimittelwert, Comment. Math. Hel. 10 (1938), 226-227.
 
[14]  A. Qayyum, M. Shoaib, A. E. Matouk, and M. A. Latif, On New Generalized Ostrowski Type Integral inequalities, Abstract and Applied Analysis, Volume 2014, Article ID 275806.
 
[15]  A. Qayyum, M. Shoaib, and I. Faye, Some New Generalized Results on Ostrowski Type Integral Inequalities With Application, Journal of computational analysis and applications, vol. 19, No.4, 2015.
 
[16]  A. Qayyum, I. Faye, M. Shoaib, M.A. Latif, A Generalization of ostrowski type inequality for mappings whose second derivatives belong to L1(a,b) and applications, International Journal of Pure and Applied Mathematics, 98 (2) 2015, 169-180.
 
[17]  A. Qayyum, M. Shoaib, M.A. Latif, A Generalized inequality of Ostrowski type for twice differentiable bounded mappings and applications, Applied Mathematical Sciences, Vol. 8, 2014, (38), 1889-1901.
 
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Article

On Quasi Multiplicative Function

1Department of Mathematics, Gauhati University, Guwahati, India


Turkish Journal of Analysis and Number Theory. 2015, 3(2), 68-69
doi: 10.12691/tjant-3-2-6
Copyright © 2015 Science and Education Publishing

Cite this paper:
Azizul Hoque, Himashree Kalita. On Quasi Multiplicative Function. Turkish Journal of Analysis and Number Theory. 2015; 3(2):68-69. doi: 10.12691/tjant-3-2-6.

Correspondence to: Himashree  Kalita, Department of Mathematics, Gauhati University, Guwahati, India. Email: ahoque.ms@gmail.com, himashree.kalita28@gmail.com

Abstract

In this paper we introduce two new Arithmetic functions, that is, Quasi-Multiplicative (QM) and omega functions. The Omega function is based on Euler’s Phi function and is used to find the sum of coprime integers. Euler’s Phi function, Dedekind’s psi function, the sigma function and -function play significant role in this work.

Keywords

References

[1]  Atanassov, K., Notes on ,ψ and σ-functions. Part 6, Notes on Number Theory and Discrete Mathematics, Vol. 19, 2013, No. 1, 22-24.
 
[2]  Burton, D. M., Elementary Number Theory, 6th edi., Tata McGraw-Hill Pub.Com. Ltd, New Delhi.
 
[3]  Dehaye, P. O., On the structure of the group of multiplicative Arithmetic functions, Bull. Belg. Math. Soc., 9, 15-21, 2002.
 
[4]  Hoque, A. and Kalita, H., Generalised perfect numbers connected with Arithmetic functions, Math. Sci. Lett., 3(3), 249-253, 2014.
 
[5]  Missana, M. V., Some results on multiplicative functions, Notes on Number Theory and Discrete Mathematics, 16 (4), 22-24, 2010.
 
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[6]  Sivaramakrishnan, R., Classical Theory of Arithmetic Function, New York, Dekker, 1989.
 
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Article

On the Variations of Some Well Known Fixed Point Theorem in Metric Spaces

1Department of Mathematics, Sardar Patel University, Anand, Gujarat, India


Turkish Journal of Analysis and Number Theory. 2015, 3(2), 70-74
doi: 10.12691/tjant-3-2-7
Copyright © 2015 Science and Education Publishing

Cite this paper:
Krishna Patel, G M Deheri. On the Variations of Some Well Known Fixed Point Theorem in Metric Spaces. Turkish Journal of Analysis and Number Theory. 2015; 3(2):70-74. doi: 10.12691/tjant-3-2-7.

Correspondence to: Krishna  Patel, Department of Mathematics, Sardar Patel University, Anand, Gujarat, India. Email: krishnappatel10@gmail.com

Abstract

Results dealing with a Fixed Point for a map need not be continuous on a metric space, which improves a famous classical result, has been presented here, wherein the convergence aspect is duly addressed. This paper aims to present some fixed point theorems on metric spaces. It can be easily observed that these are significant improvement of some of the well-known classical result dealing with the generalization of Banach fixed point theorem. Further, here the rate of convergence aspects is duly taken care of.

Keywords

References

[1]  Azam, A. and Arshad, M., “Kannan fixed point theorem on generalized metric spaces,” The J. Nonlinear Sci. Appl., 1(1), 45-48, Jul.2008.
 
[2]  Branciari, A., “A fixed point theorem of Banach- Caccippoli type on a class of generalized metric spaces,” Publ. Math. Debrecen, 57 (1-2), 31-37, 2000.
 
[3]  Kannan, R.., “Some results on fixed points,” Bull. Calcutta Math. Soc., 60, 71-76, 1968.
 
[4]  Moradi, S. and Alimohammadi, D., “New extensions of Kannan fixed-point theorem on complete metric and generalized metric spaces,” Int. Journal of math. Analysis, 5(47), 2313-2320, 2011.
 
[5]  Moradi, S. and Omid, M., “A fixed point theorem for integral type inequality depending on another function,” Int. J. Math. Anal., 4, 1491-1499, 2010.
 
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[6]  Rhoades, B. E., “A Comparison of Various Definitions of Contractive Mappings,” Amer. Math. Soc., 226, 257-290,1977.
 
[7]  Moradi, S. and Beiranvand, A., “Fixed Point of TF-contractive Single-valued Mappings,” Iranian Journal of Mathematical sciences and informatics, 5, 25-32, 2010.
 
[8]  Jungck, G. and Rhoades, B. E., “Fixed points for set valued functions without continuity”, Indian J. pure appl. Math., 29(3), 227-238, March 1998.
 
[9]  Patel, K. and Deheri, G., “Extension of some common fixed point theorems”, International Journal of Applied Physics and Mathematics, 3(5), 329-335, Sept.2013.
 
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