Turkish Journal of Analysis and Number Theory

ISSN (Print): 2333-1100

ISSN (Online): 2333-1232

Frequency: bimonthly

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

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

Google-based Impact Factor: 2.54   Citations

Article

oo)-Contractive Mapping in Multiplicative Metric Space and Fixed Point Results

1Department of Mathematics University of Peshawar, Peshawar 25000, Pakistan


Turkish Journal of Analysis and Number Theory. 2016, 4(3), 67-73
doi: 10.12691/tjant-4-3-3
Copyright © 2016 Science and Education Publishing

Cite this paper:
Bakht Zada. (αoo)-Contractive Mapping in Multiplicative Metric Space and Fixed Point Results. Turkish Journal of Analysis and Number Theory. 2016; 4(3):67-73. doi: 10.12691/tjant-4-3-3.

Correspondence to: Bakht  Zada, Department of Mathematics University of Peshawar, Peshawar 25000, Pakistan. Email: Bakhtzada56@gmail.com

Abstract

In this manuscript we introduce new type of contraction mapping in the framework of multiplicative metric space and some fixed point results. Also some example for the support of our constructed results.

Keywords

References

[1]  Banach, Sur les operations dans les ensembles abstrait et leur application aux equations integrales. Fundam. Math.3, 133-181, (1922).
 
[2]  Bashirov, Kurpunar, Ozyapici, Multiplicative calculus and its applications. Math. Anal. Appl. 337, 36-48, (2008).
 
[3]  Chatterjea, Fixed point theorems. Acad. Bulgare Sci. 25, 727-730, (1972).
 
[4]  Ghosh, A generalization of contraction principle. Int. J. Math. Math. Sci. 4(1), 201-207, (1981).
 
[5]  Kannan, Some results on fixed points. Calcutta Math. Soc. 60, 71-76, (1968).
 
Show More References
[6]  Kannan, Some results on fixed points. II. Math. Mon. 76, 405-408, (1969).
 
[7]  B. Samet, C. Vetro, and P. Vetro, Fixed point theorems for α-ψ-contractive type mappings,. Nonlinear Analysis: Theory, Methods and Applications, vol. 75, no. 4, pp. 2154-2165, (2012).
 
[8]  Shioji, N, Suzuki, T, Takahashi, Contractive mappings, Kannan mappings and metric completeness. Proc. Am. Math.Soc. 126, 3117-3124, (1998).
 
[9]  Subrahmanyam, Completeness and fixed-points. Monatshefte Math. 80, 325-330, (1975).
 
[10]  Ozavsar, Cevikel, Fixed points of multiplicative contraction mappings on multiplicative metric spaces. arXiv:1205.5131v1 [math.GM] (2012).
 
[11]  Zamfirescu, Fixed point theorems in metric spaces. Arch. Math. 23, 292-298, (1972).
 
Show Less References

Article

A Note on the Translated Whitney Numbers and Their q-Analogues

1Department of Mathematics, Mindanao State University-Main Campus, 9700 Marawi City, Philippines

2Department of Natural Sciences and Mathematics, Mindanao State University-Maigo School of Arts and Trades, 9206 Maigo, Lanao del Norte, Philippines


Turkish Journal of Analysis and Number Theory. 2016, 4(3), 74-81
doi: 10.12691/tjant-4-3-4
Copyright © 2016 Science and Education Publishing

Cite this paper:
Mahid M. Mangontarum, Omar I. Cauntongan, Amerah M. Dibagulun. A Note on the Translated Whitney Numbers and Their q-Analogues. Turkish Journal of Analysis and Number Theory. 2016; 4(3):74-81. doi: 10.12691/tjant-4-3-4.

Correspondence to: Mahid  M. Mangontarum, Department of Mathematics, Mindanao State University-Main Campus, 9700 Marawi City, Philippines. Email: mmangontarum@yahoo.com, mangontarum.mahid@msumain.edu.ph

Abstract

This paper presents natural q-analogues for the translated Whitney numbers. Several combinatorial properties which appear to be q-deformations of those classical ones are obtained. Moreover, we give a combinatorial interpretation of the classical translated Whitney numbers of the first and second kind, and their q-analogues in terms of A-tableaux.

Keywords

References

[1]  H. Belbachir and I. Bousbaa, Translated Whitney and r-Whitney numbers: a combinatorial approach, J. Integer Seq, 16 (2013), Article 13.8.6.
 
[2]  M. Benoumhani, On Whitney numbers of Dowling lattices, Discrete Math., 159 (1996), 13-33.
 
[3]  M. Benoumhani, On some numbers related to the Whitney numbers of Dowling lattices, Adv. Appl. Math., 19 (1997), 106-116.
 
[4]  M. Benoumhani, Log-concavity of Whitney numbers of Dowling lattices, Adv. Appl. Math.,22 (1999), 186-189.
 
[5]  L. Carlitz, q-Bernoulli numbers and polynomials, Duke Math. J., 15 (1948), 987-1000.
 
Show More References
[6]  C. Chen and K. Koh, Principles and Techniques in Combinatorics, Singapore, 1992.
 
[7]  R. B. Corcino and C. Barrientos, Some theorems on the q-analogue of the generalized Stirling numbers, Bull. Malays. Math. Sci. Soc., 34 (2011), 487-501.
 
[8]  R. B. Corcino, L. C. Hsu and E. L. Tan, A q-analogue of generalized Stirling numbers, Fibonacci Quart., 44 (2006), 154-167.
 
[9]  R. B. Corcino and M. M. Mangontarum, On Euler and Heine distributions and the generalized q-factorial moments, Southeast Asian Bull. Math., 38 (2014), 627-640.
 
[10]  R. B. Corcino and M. M. Mangontarum, On multiparameter q-noncentral Stirling and Bell numbers, Ars Combin., 118 (2015), 201-220.
 
[11]  H. W. Gould, The q-Stirling numbers of the first and second kinds, Duke Math. J., 28 (1994), 281-289.
 
[12]  L. Hsu and P. J. Shiue, A unified approach to generalized Stirling numbers, Adv. Appl. Math., 20(1998), 366-384.
 
[13]  J. Katriel, Combinatorial aspects of Boson algebra, Lett. Nuovo Cimento, 10 (1974), 565-567.
 
[14]  J. Katriel and M. Kibler, Normal ordering for deformed boson operators and operator-valued deformed Stirling numbers, J. Phys. A: Math. Gen., 25 (1992), 2683-2691.
 
[15]  M. M. Mangontarum and A. M. Dibagulun, On the translated Whitney numbers and their combinatorial properties, British Journal of Applied Science and Technology, 11 (2015), 1-15.
 
[16]  M. M. Mangontarum and J. Katriel, On q-boson operators and q-analogues of the r-Whitney and r-Dowling numbers, J. Integer Seq., 18 (2015), Article 15.9.8.
 
[17]  M. M. Mangontarum, A. P. M.-Ringia, and N. S. Abdulcarim, The translated Dowling polynomials and numbers, International Scholarly Research Notices, 2014, Article ID 678408, 8 pages, (2014).
 
[18]  T. Mansour, M. Schork and M. Shattuck, On a new family of generalized Stirling and Bell numbers, The Electronic Journal of Combinatorics, 18 (2011), #P77.
 
[19]  A. de Mèdicis and P. Leroux, Generalized Stirling umbers, convolution formulae and p;q-analogues, Canad. J. Math., 47 (1995), 474-499.
 
[20]  I. Mező, A new formula for the Bernoulli polynomials, Results Math., 58 (2010), 329-335.
 
[21]  J. Stirling, Methodus Differentialissme Tractus de Summatione et Interpolatione Serierum Infinitarum, London, 1730.
 
Show Less References

Article

QK Classes in Clifford Analysis

1Department of Mathematics, Faculty of Science, Jazan University, Jazan, Saudi Arabia


Turkish Journal of Analysis and Number Theory. 2016, 4(3), 82-86
doi: 10.12691/tjant-4-3-5
Copyright © 2016 Science and Education Publishing

Cite this paper:
M. A. Bakhit. QK Classes in Clifford Analysis. Turkish Journal of Analysis and Number Theory. 2016; 4(3):82-86. doi: 10.12691/tjant-4-3-5.

Correspondence to: M.  A. Bakhit, Department of Mathematics, Faculty of Science, Jazan University, Jazan, Saudi Arabia. Email: mabakhit@jazanu.edu.sa

Abstract

In this paper, we define the classes QK of quaternion-valued functions, then we characterize quaternion Bloch functions by quaternion QK functions in the unit ball of , Further, some important basic properties of these functions are also considered.

Keywords

References

[1]  F. Brackx, R. Delanghe and F. Sommen, Clifford Analysis, Pitman Research Notes in Math. Boston, London,Melbourne, 1982.
 
[2]  A. El-Sayed Ahmed, On weighted α-Besov spaces and α-Bloch spaces of quaternion-valued functions, Numer. Funct. Anal. Optim. 29 (9-10), 1046-1081, 2008.
 
[3]  A. A. El-Sayed Ahmed, Hyperholomorphic Q Classes, Math. Comput. Modelling, 55 (2012), 1428-1435.
 
[4]  A. El-Sayed Ahmed and M.A. Bakhit, Holomorphic NK and Bergman-type spaces, Birkhuser Series on Operator Theory: AdVances and Applications (2009), BirkhuserVerlag Publisher BaselSwitzerland, 195, 2009, 121-138.
 
[5]  M. Essen and H. Wulan, On analytic and meromorphic functions and spaces of QK type, Illinois J. Math.46, 2002, 1233-1258.
 
Show More References
[6]  M. Essn, H. Wulan, and J. Xiao, Several function-theoretic characterizations of Möbius invariant QK spaces, Journal of Functional Analysis, 230(1), 2006, 78-115.
 
[7]  K. Gürlebeck, U. Kähler, M. Shapiro, and L.M. Tovar, On QP spaces of quaternion-valued functions, Complex Variables Theory Appl.39, 1999, 115-135.
 
[8]  K. Gürlebeck and W. Sprӧssig, Quaternionic and Clifford Calculus for Engineers and Physicists, John Wiley &. Sons, Chichester, 1997.
 
[9]  M. M. Khalaf and M. A. Bakhit, Application of Hardy Toeplitz operators on the space of analytic functions of bounded mean oscillation in the unit all, Journal of Mathematical Analysis, 7(3), 2016, 21-32.
 
[10]  A.G. Miss, L.F. Resndis, L.M. Tovar, Quaternionic F(p,q,s) function spaces, Complex Anal. Oper. Theory, 9, 2015, 999-1024.
 
[11]  F. Pérez-Gonzáles and J. Rättyá, Univalent functions in the Möbius invariant QK space, Abstract and Applied Analysis, 2011 (2011), Article ID 259796, 11 pages.
 
[12]  L.F. Reséndis and L.M. Tovar, Besov-type characterizations for Quaternionic Bloch functions, In: Le Hung Son et al (Eds) finite or infinite complex Analysis and its applications, Adv. Complex Analysis and applications, Boston MA: Kluwer Academic Publishers, 2004, 207-220.
 
[13]  J. Ryan, Conformally covariant operators in Clifford analysis, Z. Anal. Anwend. 14 (4), 1995, 677-704.
 
[14]  A.E. Shammaky and M.A. Bakhit, Properties of weighted composition operators on some weighted holomorphic function classes in the unit ball, International Journal of Analysis and Applications, accepted.
 
[15]  A. Sudbery, Quaternionic analysis, Math. Proc. Cambridge Philos. Soc. 85, 1979, 199-225.
 
[16]  H. Wulan, Multivalent functions and QK spaces, International Journal of Mathematics and Mathematical Sciences, 45-48, 2004, 2537-2546.
 
[17]  H. Wulan and P. Wu, Characterizations of QT spaces, J. Math. Anal. Appl. 254, 2001, 484-497.
 
[18]  H. Wulan and J. Zhou, QK type spaces of analytic functions, J. Funct. Spaces Appl. 4 (1), 2006, 37-84.
 
Show Less References