Search results for "integral"
showing 10 items of 902 documents
A fixed point theorem for a Meir-Keeler type contraction through rational expression
2013
In this paper, we establish a new fixed point theorem for a Meir-Keeler type contraction through rational expression. The presented theorem is an extension of the result of Dass and Gupta (1975). Some applications to contractions of integral type are given.
Indefinite integrals of quotients of special functions
2018
ABSTRACTA new method is presented for deriving indefinite integrals involving quotients of special functions. The method combines an integration formula given previously with the recursion relations obeyed by the function. Some additional results are presented using an elementary method, here called reciprocation, which can also be used in combination with the new method to obtain additional quotient integrals. Sample results are given here for Bessel functions, Airy functions, associated Legendre functions and the three complete elliptic integrals. All results given have been numerically checked with Mathematica.
A note on the isoperimetric inequality
2003
We show that the sharp integral form on the isoperimetric inequality holds for those orientation-preserving mappings f ∈ W l o c n 2 n + 1 ( Ω , R n ) f\in W^\frac {n^2}{n+1}_{loc}(\Omega , \mathbb {R}^n) whose Jacobians obey the rule of integration by parts.
Some new fixed point theorems in Menger PM-spaces with application to Volterra type integral equation
2014
Abstract We establish some fixed point theorems by introducing two new classes of contractive mappings in Menger PM-spaces. First, we prove our results for an α - ψ -type contractive mapping and then for a generalized β -type contractive mapping. Some examples and an application to Volterra type integral equation are given to support the obtained results.
Hybrid coincidence and common fixed point theorems in Menger probabilistic metric spaces under a strict contractive condition with an application
2014
Abstract We prove some coincidence and common fixed point theorems for two hybrid pairs of mappings in Menger spaces satisfying a strict contractive condition. An illustrative example is given to support the genuineness of our extension besides deriving some related results. Then, we establish the corresponding common fixed point theorems in metric spaces. Finally, we utilize our main result to obtain the existence of a common solution for a system of Volterra type integral equations.
On the Minimal Solution of the Problem of Primitives
2000
Abstract We characterize the primitives of the minimal extension of the Lebesgue integral which also integrates the derivatives of differentiable functions (called the C -integral). Then we prove that each BV function is a multiplier for the C -integral and that the product of a derivative and a BV function is a derivative modulo a Lebesgue integrable function having arbitrarily small L 1 -norm.
Common fixed points for α-ψ-φ-contractions in generalized metric spaces
2014
We establish some common fixed point theorems for mappings satisfying an α-ψ-ϕcontractive condition in generalized metric spaces. Presented theorems extend and generalize manyexisting results in the literature.
 Erratum to “Common fixed points for α-ψ-φ-contractions in generalized metric spaces”
 In Example 1 of our paper [V. La Rosa, P. Vetro, Common fixed points for α-ψ-ϕcontractions in generalized metric spaces, Nonlinear Anal. Model. Control, 19(1):43–54, 2014] a generalized metric has been assumed. Nevertheless some mistakes have appeared in the statement. The aim of this note is to correct this situation.
Multidimensional dyadic Kurzweil–Henstock- and Perron-type integrals in the theory of Haar and Walsh series
2015
Abstract The problem of recovering the coefficients of rectangular convergent multiple Haar and Walsh series from their sums, by generalized Fourier formulas, is reduced to the one of recovering a function (the primitive) from its derivative with respect to the appropriate derivation basis. Multidimensional dyadic Kurzweil–Henstock- and Perron-type integrals are compared and it is shown that a Perron-type integral, defined by major and minor functions having a special continuity property, solves the coefficients problem for series which are convergent everywhere outside some uniqueness sets.
Krasnosel'skiĭ-Schaefer type method in the existence problems
2019
We consider a general integral equation satisfying algebraic conditions in a Banach space. Using Krasnosel'skii-Schaefer type method and technical assumptions, we prove an existence theorem producing a periodic solution of some nonlinear integral equation.
Integration of both the derivatives with respect to P-paths and approximative derivatives
2009
In the present paper, in terms of generalized absolute continuity, we present a descriptive characteristic of the primitive with respect to a system of P-paths and study the relationship between the Denjoy-Khinchin integral and the Henstock H P-integral. © 2009 Pleiades Publishing, Ltd.