List of Articles قضیه نقطه ثابت داربو

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  1 - A new characterization for Meir-Keeler condensing operators and its applications
  H. Khandani F. Khojasteh
  Darbo's fixed point theorem and its generalizations play a crucial role in the existence of solutions in integral equations. Meir-Keeler condensing operators is a generalization of Darbo's fixed point theorem and most of other generalizations are a special case of this More

  Darbo's fixed point theorem and its generalizations play a crucial role in the existence of solutions in integral equations. Meir-Keeler condensing operators is a generalization of Darbo's fixed point theorem and most of other generalizations are a special case of this result. In recent years, some authors applied these generalizations to solve several special integral equations and some of them presented a characterization for Meir-Keeler condensing operators, which needs L-functions. But, finding an appropriate L-function needs more struggle. In this paper, we give a characterization for Meir-Keeler condensing operators via measure of non-compactness. Current characterization presents a criterion by which we can show that if a given generalization of Darbo's fixed point theorem is Meer-Keeler condensing or not. Ultimately, we give several corollaries and point out several generalizations of Darbo's fixed point theorem and show that all of them are Meir-Keeler condensing operator or a special case of this result. Manuscript profile
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  2 - Solvability of Functional Integral-Differential Equations in the Sobolev space w^{k,infinity}(R^n)
  Masoome Hosseini Farahi Mahmoud Hassani Reza Allahyari
  In 1930, Kuratowski introduced the concept of measure of noncompactness. Later, Banas and Goebel generalized this concept axiomatically, which is more convenient in applications. The principal application of measures of noncompactness in fixed point theory is contained More

  In 1930, Kuratowski introduced the concept of measure of noncompactness. Later, Banas and Goebel generalized this concept axiomatically, which is more convenient in applications. The principal application of measures of noncompactness in fixed point theory is contained in the Darbo'sfixed point theorem. This is a tool to investigate the existence and behaviour of solutions of manyclasses of integral equations such as Volterra, Fredholm and Uryson types.The technique of measure of noncompactness is applicable in several branches of nonlinear analysis. In particular, it is a very useful tool for several types of integral and integral-differential equations. In addition, the measure of noncompactness is also used in functional equations, fractional partial differential equations, ordinary and partial differential equations, operator theory and optimal control theory. The purpose of this article is to introduce a new measure of noncompactness in the Sobolev space W^(k,∞) (R^n). The results are obtained to solve integral-differential equations. Finally, by providing an example to show the efficiency of our results. Manuscript profile