Common Fixed Point Point Theorem for a Pair of Weakly Compatible Mappings on Banach Spaces (original) (raw)

Abstract. In this paper, we prove a common xed point theorem fornoncompatible, discontinuous mappings on a Banach space. Our maintheorem extends, improves, generalizes some known results on Banachspaces. 1. Introduction and PreliminariesHusain and Sehgal [1] proved common xed point theorems for a familyof mappings. Khan and Imdad [5] extended result of Husain and Sehgal [1].Imdad, Khan and Sessa [2] extended above results and proved common xedpoints for three mappings de ned on a closed subset of a uniformly convexBanach space.Rashwan [9] extended result of Imdad, Khan and Sessa [2] by employingfour compatible mappings of type (A) instead of weakly commuting mappingsand by using one continuous mapping as opposed to two.Sharma and Bamboria [12] improved results of Rashwan [9] by removingthe condition of continuity and replacing the compatibility of mappings of type(A) by weak compatibility. Sharma and Tilwankar [13] proved a common xedpoint theorem for four mappings under the conditi...