$rho$-Attractive Elements in Modular Function Spaces
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Authors: H. IQBAL, M. ABBAS AND S. H. KHAN
DOI: 10.46793/KgJMat2101.047I
Abstract:
In this paper, we introduce the notion of ρ-attractive elements in modular function spaces. A new class of mappings called ρ-k-nonspreading mappings is also introduced. Making a good use of the two notions, we first prove existence results and then some approximation results in the setup of modular function spaces. An example is presented to support the results proved herein.
Keywords:
Attractive points, modular spaces, nonspreading mappings, modular functions.
References:
[1] W. I. A. Kaewkhao and K. Kunwai, Attractive points and convergence theorems for normally generalized hybrid mappings in cat (0) spaces, Fixed Point Theory Appl. 2015(1) (2015), 14 pages.
[2] B. A. B. Dehaish and W. M. Kozlowski, Fixed point iteration processes for asymptotic pointwise nonexpansive mapping in modular function spaces, Fixed Point Theory Appl. 2012(118) (2012), 23 pages.
[3] A. Ilchev and B. Zlatanov, Fixed and best proximity points for kannan cyclic contractions in modular function spaces, J. Fixed Point Theory Appl. 9 (2017), 2873–2893.
[4] A. Ilchev and B. Zlatanov, Coupled fixed points and coupled best proximity points in modular function spaces, International Journal of Pure and Applied Mathematics 118 (2018), 957–977.
[5] A. K. K. Kunwai and W. Inthakon, Properties of attractive points in cat (0) spaces, Thai J. Math. 13 (2015), 109–121.
[6] M. A. Khamsi, Convexity property in modular function spaces, Sci. Math. Jpn. 44 (1996), 269–280.
[7] M. A. Khamsi and W. M. Kozolowski, Fixed Point Theory in Modular Function Spaces, Springer, Berlin, 2015.
[8] F. Kohsaka and W. Takahashi, Fixed point theorems for a class of nonlinear mappings related to maximal monotone operators in banach spaces, Arch. Math. 91 (2008), 166–177.
[9] W. M. Kozlowski, Advancements in fixed point theory in modular function spaces, Arab. J. Math. 1 (2012), 477–494.
[10] K. Kuaket and P. Kumam, Fixed points of asymptotic pointwise contractions in modular spaces, Appl. Math. Lett. 24 (2011), 1795–1798.
[11] M. A. Khamsi, W. M. Kozlowski and S. Reich, Fixed point theory in modular function spaces, Nonlinear Anal. 14 (1990), 935–953.
[12] J. Musielak and W. Orlicz, On modular spaces, Studia Math. 18 (1959), 49–65.
[13] H. Nakano, Modular Semi-Ordered Spaces, Maruzen, Tokyo, 1950.
[14] S. H. Khan, M. Abbas and S. Ali, Fixed point approximation of multivalued ρ-quasi-nonexpansive mappings in modular function spaces, J. Nonlinear Sci. Appl. 10 (2017), 3168–3179.
[15] S. Suantai, P. Cholamjiak, Y. J. Cho and W. Cholamjiak, On solving split equilibrium problems and fixed point problems of nonspreading multi-valued mappings in hilbert spaces, Fixed Point Theory Appl. 2016 (2016), 35.
[16] W. Takahashi and Y. Takeuchi, Nonlinear ergodic theorem without convexity for generalized hybrid mappings in a hilbert space, J. Nonlinear Convex Anal. 12 (2011), 399–406.
[17] W. Takahashi, N. C. Wong and J. C. Yao, Attractive point and weak convergence theorems for new generalized hybrid mappings in Hilbert spaces, J. Nonlinear Convex Anal. 13 (2012), 745–757.
[18] Y. Zheng, Attractive points and convergence theorems of generalized hybrid mapping, J. Nonlinear Sci. Appl. 8 (2015), 354–362.
[19] B. Zlatanov, Best proximity points in modular function spaces, Arab. J. Math. 4 (2015), 215–227.
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