Abstract
We prove the existence theorem of fixed points for a generalized weak contractive mapping in modular spaces.
Highlights
In 1997, Alber and Guerre-Delabriere [1] introduced the concept of weak contraction in Hilbert spaces
Even though a metric is not defined, many problems in metric fixed point theory can be reformulated in modular spaces
Let Xρ be a modular space in which ρ satisfies the Δ 2-condition and let {xn}n∈N be a sequence in Xρ
Summary
In 1997, Alber and Guerre-Delabriere [1] introduced the concept of weak contraction in Hilbert spaces. Rhoades [2] proved that the result which Alber et al is valid in complete metric spaces, the result of Rhoades in the following: A mapping T : X → X where (X, d) is a metric space, is said to be weakly contractive if d (T (x) , T (y)) ≤ d (x, y) − φ (d (x, y)) ,. In 2008, Dutta and Choudhury [3] introduced a new generalization of contraction in metric spaces and proved the following theorem. Even though a metric is not defined, many problems in metric fixed point theory can be reformulated in modular spaces. We will study the existence of fixed point theorems for mappings satisfying generalized weak contraction mappings in modular spaces
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