1,721,176 research outputs found
On (ψ,ϕ)-weakly contractive condition in partially ordered metric spaces
No full textAbstractRecently, Heman Kumar Nashine and Bessem Samet [H.K. Nashine, B. Samet, Fixed point results for mappings satisfying (ψ,ϕ)-weakly contractive condition in partially ordered metric spaces, Nonlinear Anal. 74 (2011) 2201–2209] studied some coincidence fixed point and common fixed point theorems for two mappings satisfying (ψ,ϕ)-weakly contractive condition in an ordered complete metric space. In the present paper, we study some coincidence fixed point and common fixed point theorems for three mappings S,T and R satisfying (ψ,ϕ)-weakly contractive condition in an ordered complete metric space, where the mappings S and T are assumed to be weakly increasing with respect to R. Our results generalize several well-known results in the literature
Common fixed point under contractive condition of Ciric's type in cone metric spaces
No full textA common fixed point theorem is established for a pair of self-mappings of a
complete cone metric space. The obtained result is an extension of Ljubomir
Ciric?s theorem [Lj. Ciric: On common fixed points in uniform spaces, Publ.
Inst. Math. 24 (38) (1978), 39[43].</jats:p
On an implicit convexity concept and some integral inequalities
No full textAbstract We introduce a new concept of convexity that depends on a function F : R × R × R × ( 0 , 1 ) → R satisfying certain axioms. The presented concept generalizes many kinds of convexity including ε-convex functions, α-convex functions, and h-convex functions. Moreover, some integral inequalities are provided via our notion of convexity
Fejér-Type Inequalities for Some Classes of Differentiable Functions
No full textWe let υ be a convex function on an interval [ι1,ι2]⊂R. If ζ∈C([ι1,ι2]), ζ≥0 and ζ is symmetric with respect to ι1+ι22, then υ12∑j=12ιj∫ι1ι2ζ(s)ds≤∫ι1ι2υ(s)ζ(s)ds≤12∑j=12υ(ιj)∫ι1ι2ζ(s)ds. The above estimates were obtained by Fejér in 1906 as a generalization of the Hermite–Hadamard inequality (the above inequality with ζ≡1). This work is focused on the study of right-side Fejér-type inequalities in one- and two-dimensional cases for new classes of differentiable functions υ. In the one-dimensional case, the obtained results hold without any symmetry condition imposed on the weight function ζ. In the two-dimensional case, the right side of Fejer’s inequality is extended to the class of subharmonic functions υ on a disk
Ran-Reurings fixed point theorem is an immediate consequence of the Banach contraction principle
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