A FIXED POINT THEOREM FOR MAPPINGS SATISFYING A GENERAL CONTRACTIVE CONDITION OF INTEGRAL TYPE

By A. Branciari. 2002

604 citations recorded by the source corpus.

We analyze the existence of fixed points for mappings defined on complete metric spaces (X,d) satisfying a general contractive inequality of integral type. This condition is analogous to Banach-Caccioppoli's one; in short, we study mappings f:X→X for which there exists a real number c∈]0,1[, such that for each x,y∈X we have ∫0d(fx,fy)φ(t)dt≤c∫0d(x,y)φ(t)dt, where φ:[0,

Subfields: Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/8430cb976da2111066030ad4faf933faa839bc9b

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In Geometry and Topology

Citations in the corpus

A FIXED POINT THEOREM IN A GENERALIZED METRIC SPACE FOR MAPPINGS SATISFYING A CONTRACTIVE CONDITION OF INTEGRAL TYPE (2009, background): “(10) In fact, if there exists a subsequence (pk) ⊂ N, pk > k, d(fkx, fkx) ≥ ε, we obtain ε ≤ d(fkx, fkx) ≤ d(fkx, fkx) + d(fkx, fkx) + d(fkx, fkx) → ε as k → +∞, and from (2) ∫ d(fm(pk)+1x,fn(pk)+1x)”
Fixed Points of Weakly Compatible Maps Satisfying a General Contractive Condition of Integral Type (2007, background): “This result substantially extends the theorems of [1, 4, 6].”
Fixed point theorems for mappings satisfying contractive conditions of integral type and applications (2011, methodology): “In 2002, Branciari [8] gave an integral version of the Banach contraction principles and showed the following fixed point theorem.”
Altering Distance and Common Fixed Points under Implicit Relations (2009, background): “[4] Let (X, d) be a complete metric space, c ∈ (0, 1) and f : X → X a mapping such that, for each x, y ∈ X,”
Fixed point theorems for multivalued maps in cone metric spaces (2011, background): “Because of its importance for mathematical theory, Banach contraction principle has been extended in many direction (see [1-8]).”
SOME FIXED POINT THEOREMS FOR WEAKLY COMPATIBLE MAPPINGS SATISFYING AN IMPLICIT RELATION (2009, background): “In [5] Branciari proved the following interesting result for fixed point theory.”
Gregus type fixed points for a tangential multi-valued mappings satisfying contractive conditions of integral type (2011, background): “Since there exists two sequences xn = 1 + 1 n and yn = 1 − 1n such that lim n→∞ f xn = lim n→∞ f yn = 2 and 2 ∈ [2, 3] = lim n→∞n = lim n→∞n Therefore the mapping f is tangential w.”
Two fixed-point theorems for mappings satisfying a general contractive condition of integral type (2003, result): “These results substantially extend the theorem of Branciari (2002).”
Common Fixed Point Theorems for Hybrid Pairs of Occasionally Weakly Compatible Mappings Satisfying Generalized Contractive Condition of Integral Type (2007, background): “Branciari [5] obtained a fixed point theorem for a single valued mapping satisfying an analogue of Banach’s contraction principle for an integral-type inequality.”