Jñānābha‎, Vol. 49 (1) (2019), 67-79

A COMMON FIXED POINT THEOREM FOR WEAKLY RECIPROCALLY CONTINUOUS SYSTEMS OF MAPS SATISFYING A GENERAL CONTRACTIVE CONDITION OF INTEGRAL TYPE

Deepak Khantwal* and U.C. Gairola

*Department of Mathematics,
Graphic Era Hill University, Dehradun-248002, Uttarakhand, India
Department of Mathematics,
H.N.B. Garhwal University, BGR Campus, Pauri Garhwal-246001, Uttarakhand, India
Email:deepakkhantwal15@gmail.com*, ucgairola@rediffmail.com
(Received : May 15, 2019 ; Revised: May 24, 2019)



Abstract

In this paper we prove a common .fixed point theorem for weakly reciprocally continuous systems of maps satisfying a general contractive inequality of integral type on the finite product of metric spaces. Our result generalizes the results of Branciari [2], Rhoades [25], Matkowski [17] and Gairola [5].


2010 Mathematics Subject Classifications47H10, 54H25.
Keywords and phrasesFixed point, coordinatewise commuting maps, weakly commuting maps, asymptotically commuting maps, weak reciprocal continuous maps and product space.