Some Fixed point and common Fixed point Theorems in 2- Banach Spaces

Abstract

In this paper we presents some theorems in 2 Banach spaces. Mathematics subject classification: 47H10, 54H25. I. Introduction: A large variety of the problems of analysis and applied mathematics reduce to finding solutions of non linear functional equations which can be formulated in terms of finding the fixed points of a non linear mapping. Fixed point theorems are very important tools for proving the existence and uniqness of the solutions to various differential, integral and partial differential equations and variational inequalities etc. representing phenomena arising in different fields. Therefore the fixed point methods specially Banach's contraction principle provides a powerful tool for obtaining the solutions of these equations which were very difficult to solve by any other methods. Recently described about the application of Banach's contraction principle (2). Ghalar (4) introduced the concept of 2- Banach. Recently Badshah and Gupta (3), Yadava, Rajput and Bhardwaj (6) and Yadav, Rajput, Choudhary and Bhardwaj (7) also worked for Banach and 2-Banach spaces for non contraction mapping. In present paper we prove some fixed point theorems for non-contraction mappings, in 2-Banach spaces motivated by above, before starting the main result first we write some definitions