Picard and weakly Picard operators technique for nonlinear differential equations in Banach spaces
Journal of Mathematical Analysis and Applications, 2012 The authors study nonlocal Cauchy problems for differential equations in Banach spaces. Using Picard and weakly Picard operators technique and suitable Bielecki norms, some existence, uniqueness and data dependence results are obtained under some mild conditions. They also discuss a class of impulsive Cauchy problems by adapting the same methods.
Jinrong Wang, Yong Zhou, M. Medveď
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ON A NEW CLASS OF MULTIVALUED WEAKLY PICARD OPERATORS ON COMPLETE METRIC SPACES
Taiwanese Journal of Mathematics, 2015 In the present paper, the concept of nonlinear $F$-contraction formultivalued mappings in metric spaces is introduced and considering the new proof technique, which was used for single valued maps by Wardowski [D. Wardowski, Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl.
I. Altun, M. Olgun, Gülhan Minak
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A class of abstract Volterra equations, via weakly Picard operators technique [PDF]
Mathematical Inequalities & Applications, 2010 Summary: We consider the following abstract Volterra equations: \[ x(t) = G(t,g(x)(t),x(t),x(0)) + \int ^t_{-t} K (t,s,x(s),x(h(s)))\,ds,\quad t \in \mathbb R \] and \[ x(t) = G(t,g(x)(t),x(t),x(0)) + \int ^{|t|}_{-|t|} K (t,s,x(s),x(h(s)))\,ds,\quad t \in\mathbb R.
M. Serban, I. Rus, A. Petruşel
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ON THE SOLUTION OF STEINHAUS FUNCTIONAL EQUATION USING WEAKLY PICARD OPERATORS
Filomat, 2011 In this paper we obtain existence results regarding the solutions g of a Steinhaus type functional equation of the form g(x)+ g(f(x))= F(x), under the significantly weaker assumption that f is a weakly Picard operator. The solutions are given in terms of sums of either convergent series or divergent series but summable by some method of ...
V. Berinde
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Implicit functional differential equations with linear modification of the argument, via weakly Picard operator theory [PDF]
Carpathian Journal of Mathematics, 2021 "Let \mathbf{K}:=\mathbf{R}\text{ or }\mathbf{C},\text{ \ }0<\lambda <1 and f \in C([0,b] \times \textbf{K}^3,\textbf{K}). In this paper we use the weakly Picard operator theory technique to study the following functional-differential equation $$ y'(x)=f(x,y(x),y'(x),y(\lambda x)), x \in [0,b].$$ "
ANTON S. MUREŞAN, VIORICA MUREŞAN
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Data dependence results of a new multistep and S-iterative schemes for contractive-like operators [PDF]
, 2012 In this paper, we prove that convergence of a new iteration and S-iteration can be used to approximate to the fixed points of contractive-like operators.
Gursoy, Faik +2 more
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Fixed Point Results for Frum-Ketkov Type Contractions in b-Metric Spaces
Axioms, 2021 The purpose of this paper is to present some fixed point results for Frum-Ketkov type operators in complete b-metric spaces.
Cristian Chifu +2 more
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Fractional differential equations with maxima on time scale via Picard operators
Filomat, 2023 In this paper, we prove a result of existence and uniqueness of solutions for the following class of problem of initial value for differential equations with maxima and Caputo?s fractional order on the time scales: c??a u(?) = ?(?, u(?), max ??[a,?] u(
E. Karapınar +3 more
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The Theory of Reich's Fixed Point Theorem for Multivalued Operators
Fixed Point Theory and Applications, 2010 The purpose of this paper is to present a theory of Reich's fixed point theorem for multivalued operators in terms of fixed points, strict fixed points, multivalued weakly Picard operators, multivalued Picard operators, data dependence of the fixed ...
Tania Lazăr +3 more
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Nonperturbative Effective Actions of N=2 Supersymmetric Gauge Theories [PDF]
, 1995 We elaborate on our previous work on N=2 supersymmetric Yang-Mills theory. In particular, we show how to explicitly determine the low energy quantum effective action for $G=SU(3)$ from the underlying hyperelliptic Riemann surface, and calculate the ...
Klemm, A., Lerche, W., Theisen, S.
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