In the present paper, we prove a coupled coincidence fixed point theorem in the setting of a generalized metric space in the sense of Z.
📌 3 Maddede Bu Makale
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Amaç & Hipotez:Lakshmikantham (Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Analysis 65, 1379–1393, 2006), V.
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Temel Bulgular & Veri:Ciri´c ( ´ Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Analysis 70, (2009) 4341–4349, 2009) introduced the concept of a coupled coincidence point of a mapping F from X ×X into X and a mapping g from X into X.
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Sonuç & Katkı:In the present paper, we prove a coupled coincidence fixed point theorem in the setting of a generalized metric space in the sense of Z.
🔬Tür:Araştırma Makalesi
📍Kapsam:2006 Verileri
⚙️Değişkenler:Common fixed Point · Coupled coincidence fixed point · Generalized metric space
Abstract
T. G. Bhaskar and V. Lakshmikantham (Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Analysis 65, 1379–1393, 2006), V. Lakshmikantham and Lj. B. Ciri´c ( ´ Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Analysis 70, (2009) 4341–4349, 2009) introduced the concept of a coupled coincidence point of a mapping F from X ×X into X and a mapping g from X into X. In the present paper, we prove a coupled coincidence fixed point theorem in the setting of a generalized metric space in the sense of Z. Mustafa and B. Sims.
SHATANAWİ, W. (2022). COUPLED FIXED POINT THEOREMS IN GENERALIZED METRIC SPACES. Hacettepe Journal of Mathematics and Statistics, Cilt: 40 - Sayı: 3, 441–447. https://ajindex.com/articles/530559
Abbas, M. and Jungck, G. Common fixed point results for noncommuting mappings without continuity in cone metric spaces, J. Math. Anal. Appl. 341, 416–420, 2008.
Abbas, M. and Rhoades, B. E. Common fixed point results for noncommuting mapping without continuity in generalized metric spaces, Applied Mathematics and Computation 215, 262–269, 2009.
Abdeljawad, Th. Completion of cone metric spaces, Hacet. J. Math. Stat. 39,67–74, 2010. [4] Beg, I. and Abbas, M. Coincidence point and invariant approximation for mappings satis- fying generalized weak contractive condition, Fixed Point Theor. Appl., Article ID 74503, 1–7, 2006.
Bhaskar, T. G and Lakshmikantham, G. V. Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Analysis 65, 1379–1393, 2006.
Haung, L. G. and Zhang, X. Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl. 332, 1468–1476, 2007.
Jungck, G. Commuting maps and fixed points, Am. Math. Monthly 83, 261–263, 1976.
Jungck, G. Compatible mappings and common fixed points, Int. J. Math. Sci. 9 (4), 771–779, 1986.
Jungck, G. Common fixed points for commuting and compatible maps on compacta, Proc. Am. Math. Soc. 103, 977–983, 1988.
Jungck, G. and Hussain, N. Compatible maps and invariant approximations, J. Math. Anal. Appl. 325 (2), 1003–1012, 2007.
Lakshmikantham, V. and ´Ciri´c, Lj. B. Coupled fixed point theorems for nonlinear contrac- tions in partially ordered metric spaces, Nonlinear Analysis 70, 4341–4349, 2009.
P. P. Murthy, P. P. and Tas, K. New common fixed point theorems of Gregus type for R- weakly commuting mappings in 2-metric spaces, Hacet. J. Math. Stat. 38, 285–291, 2009. [13] Mustafa, Z. and Sims, B. Some Remarks concerning D-metric spaces, in: Proc. Int. Conf. on Fixed Point Theor. Appl., Valencia (Spain), July 2003, pp. 189–198.
Mustafa, Z. and Sims, B. A new approach to generalized metric spaces, J. Nonlinear Convex Anal. 7 (2), 289–297, 2006.
Mustafa, Z., Shatanawi, W. and Bataineh, M. Existence of fixed point results in G-metric spaces, International Journal of Mathematics and Mathematical Sciences Volume, Article ID 283028, 10 pages, 2009.
Mustafa, Z., Obiedat, H. and Awawdeh, F. Some common fixed point theorem for mapping on complete G-metric spaces, Fixed Point Theor. Appl. Article ID 189870, 12 pages, 2008. [17] Pant, R. P. Common fixed points of noncommuting mappings, J. Math. Anal. Appl. 188, 436–440, 1994.
Popa, V. and Mocanu, M. Altering distance and common f