The Experts below are selected from a list of 13242 Experts worldwide ranked by ideXlab platform
Muhammad Sarwar - One of the best experts on this subject based on the ideXlab platform.
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Fixed Point Results Satisfying Rational Type Contraction in -Metric Spaces
Journal of Function Spaces, 2016Co-Authors: Branislav Z. Popović, Muhammad Shoaib, Muhammad SarwarAbstract:A Unique Fixed Point theorem for three self-maps under rational type contractive condition is established. In addition, a Unique Fixed Point result for six continuous self-mappings through rational type expression is also discussed.
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Fixed Point Theorems for Expanding Mappings in Dislocated Metric Space
2015Co-Authors: Muhammad SarwarAbstract:The aim of this paper is to present Fixed Point theorems in disl ocated metric space. We have proved some Unique Fixed Point results for expanding type of continuous self-mapping and surjective expanding self-map in dislocated metric space. A non-Unique Fixed Point theorem has been obtained for Hardy-Rogers type m apping using expanding mapping in dislocated metric space. Examples are given in the support of our constructed results.
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Some Unique Fixed Point Theorems in Multiplicative Metric Spaces
arXiv: General Mathematics, 2014Co-Authors: Muhammad Sarwar, Badshah-e-romeAbstract:\"{O}zavsar and Cevikel(Fixed Point of multiplicative contraction mappings on multiplicative metric space.arXiv:1205.5131v1 [math.GN] 23 may 2012)initiated the concept of the multiplicative metric space in such a way that the usual triangular inequality is replaced by "multiplicative triangle inequality $d(x,y)\leq d(x,z).d(z,y)$ for all $x,y,z\in X$". In this manuscript, we discussed some Unique Fixed Point theorems in the context of multiplicative metric spaces. The established results carry some well known results from the literature to multiplicative metric space. We note that some Fixed Point theorems can be deduced in multiplicative metric space by using the established results. Appropriate examples are also given.
Daniel W H James - One of the best experts on this subject based on the ideXlab platform.
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proving the Unique Fixed Point principle correct an adventure with category theory
International Conference on Functional Programming, 2011Co-Authors: Ralf Hinze, Daniel W H JamesAbstract:Say you want to prove something about an infinite data-structure, such as a stream or an infinite tree, but you would rather not subject yourself to coinduction. The Unique Fixed-Point principle is an easy-to-use, calculational alternative. The proof technique rests on the fact that certain recursion equations have Unique solutions; if two elements of a coinductive type satisfy the same equation of this kind, then they are equal. In this paper we precisely characterize the conditions that guarantee a Unique solution. Significantly, we do so not with a syntactic criterion, but with a semantic one that stems from the categorical notion of naturality. Our development is based on distributive laws and bialgebras, and draws heavily on Turi and Plotkin's pioneering work on mathematical operational semantics. Along the way, we break down the design space in two dimensions, leading to a total of nine Points. Each gives rise to varying degrees of expressiveness, and we will discuss three in depth. Furthermore, our development is generic in the syntax of equations and in the behaviour they encode - we are not caged in the world of streams.
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ICFP - Proving the Unique Fixed-Point principle correct: an adventure with category theory
Proceeding of the 16th ACM SIGPLAN international conference on Functional programming - ICFP '11, 2011Co-Authors: Ralf Hinze, Daniel W H JamesAbstract:Say you want to prove something about an infinite data-structure, such as a stream or an infinite tree, but you would rather not subject yourself to coinduction. The Unique Fixed-Point principle is an easy-to-use, calculational alternative. The proof technique rests on the fact that certain recursion equations have Unique solutions; if two elements of a coinductive type satisfy the same equation of this kind, then they are equal. In this paper we precisely characterize the conditions that guarantee a Unique solution. Significantly, we do so not with a syntactic criterion, but with a semantic one that stems from the categorical notion of naturality. Our development is based on distributive laws and bialgebras, and draws heavily on Turi and Plotkin's pioneering work on mathematical operational semantics. Along the way, we break down the design space in two dimensions, leading to a total of nine Points. Each gives rise to varying degrees of expressiveness, and we will discuss three in depth. Furthermore, our development is generic in the syntax of equations and in the behaviour they encode - we are not caged in the world of streams.
Branislav Z. Popović - One of the best experts on this subject based on the ideXlab platform.
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Fixed Point Results Satisfying Rational Type Contraction in -Metric Spaces
Journal of Function Spaces, 2016Co-Authors: Branislav Z. Popović, Muhammad Shoaib, Muhammad SarwarAbstract:A Unique Fixed Point theorem for three self-maps under rational type contractive condition is established. In addition, a Unique Fixed Point result for six continuous self-mappings through rational type expression is also discussed.
Ralf Hinze - One of the best experts on this subject based on the ideXlab platform.
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proving the Unique Fixed Point principle correct an adventure with category theory
International Conference on Functional Programming, 2011Co-Authors: Ralf Hinze, Daniel W H JamesAbstract:Say you want to prove something about an infinite data-structure, such as a stream or an infinite tree, but you would rather not subject yourself to coinduction. The Unique Fixed-Point principle is an easy-to-use, calculational alternative. The proof technique rests on the fact that certain recursion equations have Unique solutions; if two elements of a coinductive type satisfy the same equation of this kind, then they are equal. In this paper we precisely characterize the conditions that guarantee a Unique solution. Significantly, we do so not with a syntactic criterion, but with a semantic one that stems from the categorical notion of naturality. Our development is based on distributive laws and bialgebras, and draws heavily on Turi and Plotkin's pioneering work on mathematical operational semantics. Along the way, we break down the design space in two dimensions, leading to a total of nine Points. Each gives rise to varying degrees of expressiveness, and we will discuss three in depth. Furthermore, our development is generic in the syntax of equations and in the behaviour they encode - we are not caged in the world of streams.
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ICFP - Proving the Unique Fixed-Point principle correct: an adventure with category theory
Proceeding of the 16th ACM SIGPLAN international conference on Functional programming - ICFP '11, 2011Co-Authors: Ralf Hinze, Daniel W H JamesAbstract:Say you want to prove something about an infinite data-structure, such as a stream or an infinite tree, but you would rather not subject yourself to coinduction. The Unique Fixed-Point principle is an easy-to-use, calculational alternative. The proof technique rests on the fact that certain recursion equations have Unique solutions; if two elements of a coinductive type satisfy the same equation of this kind, then they are equal. In this paper we precisely characterize the conditions that guarantee a Unique solution. Significantly, we do so not with a syntactic criterion, but with a semantic one that stems from the categorical notion of naturality. Our development is based on distributive laws and bialgebras, and draws heavily on Turi and Plotkin's pioneering work on mathematical operational semantics. Along the way, we break down the design space in two dimensions, leading to a total of nine Points. Each gives rise to varying degrees of expressiveness, and we will discuss three in depth. Furthermore, our development is generic in the syntax of equations and in the behaviour they encode - we are not caged in the world of streams.
Badriah A. S. Alamri - One of the best experts on this subject based on the ideXlab platform.
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A sufficient and necessary condition for the convergence of the sequence of successive approximations to a Unique Fixed Point II
Fixed Point Theory and Applications, 2015Co-Authors: Tomonari Suzuki, Badriah A. S. AlamriAbstract:Using the concept of a Boyd-Wong contraction, we obtain a simple, sufficient, and necessary condition for the convergence of the sequence of successive approximations to a Unique Fixed Point.
