Fixed point theorems for generalized (beta-phi)-contractive pair of mappings using simulation functions

Manoj Kumar; Rashmi Sharma

doi:10.5269/bspm.40870

Manoj Kumar Lovely Professional University
Rashmi Sharma Lovely Professional University

Résumé

In this paper, our aim is to present a new class of generalized (beta-phi)-Z- contractive pair of mappings and we prove certain xed point theorems for a pair of mappings using this concept. Our results generalizes some xed point theorems in the literature. As an application some xed point theorems endowed with a partial order in metric spaces are also proved.

Téléchargements

Les données sur le téléchargement ne sont pas encore disponible.

Références

Banach, S.: Surles operations dans les ensembles abstraits et leur applications aux equations itegrates, Fundamenta Mathematics 3, 133-181 (1922).

Bhaskar, T. G., Lakshmikantham, V.: Fixed Point Theory in partially ordered metric spaces and applications, Nonlinear Analysis 65, 1379-1393 (2006).

Branciari, A.: A fixed point theorem for mappings satisfying a general contractive condition of integral type, Int. J. Math. Math. Sci. 29, 531-536 (2002).

Caccioppoli, R.: Un teorema generale sullesistenza di elementi uniti in una transformazione funzionale, Rendicontilincei: Mathematica E Applicazioni. 11, 794-799 (1930). (in Italian).

Ciric, L., Cakic, N., Rajovic, M., Ume, J. S.: Monotone generalized nonlinear contractions in partially ordered metric spaces, Fixed Point Theory Appl. 2008 (2008), Article ID 131294, 11 pages.

Kannan, R.: Some results on fixed points, Bull. Calcutta. Math. Soc. 10, 71-76 (1968).

Karapinar, E., Samet, B.: Generalized α − ψ− contractive type mappings and related fixed point theorems with applications, Abstract and Applied Analysis 2012 Article ID 793486, 17 pages doi: 10.1155/2012/793486.

Lakshmikantham, V., Ciric, L.: Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Analysis 70, 4341-4349 (2009).

Nieto, J. J., Lopez, R. R.: Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order 22, 223-239 (2005).

Saadati, R., Vaezpour, S. M.: Monotone generalized weak contractions in partially ordered metric spaces, Fixed Point Theory 11, 375-382 (2010).

Samet, B., Vetro, P.: Fixed point theorem for α − ψ− contractive type mappings, Nonlinear Anal. 75, 2154-2165(2012).

Shahi, P., Kaur, J., Bhatia, S. S.: Coincidence and common fixed point results for generalized α−ψ−contractive type mappings with applications, arXiv:1306.3498v1 [math.FA] 14 jun 2013.

Khojasteh F., Shukla S., Radenovic S.: A new approach to the study of ?xed point theory for simulation functions, Filomat. 29, 1189-1194.1 (2015).

Argoubi H., Samet B., Vetro C.: Nonlinear contractions involving simulation functions in a metric space with a partial order, J. Nonlinear Sci. Appl. 8, 1082-1094.1, 1.8. 1.9(2015).