scholarly journals Some New Refined General Boas-Type Inequalities

2012 ◽  
Vol 2012 ◽  
pp. 1-23
Author(s):  
A. Čižmešija ◽  
J. Pečarić ◽  
D. Pokaz
Keyword(s):  
Topological Space ◽  
Type Inequality ◽  
New Class ◽  
Borel Measures ◽  
Right Hand

We state and prove a new refined Boas-type inequality in a setting with a topological space and generalσ-finite and finite Borel measures. As a consequence of the result obtained, we derive a new class of Hardy- and Pólya-Knopp-type inequalities related to balls inℝnand prove that constant factors involved in their right-hand sides are the best possible.

scholarly journals On a topology between Tα and Tγα

Filomat ◽  
2019 ◽  
Vol 33 (10) ◽  
pp. 3209-3221
Author(s):  
Dimitrije Andrijevic
Keyword(s):  
Topological Space ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Closure Operators ◽  
New Class ◽  
Necessary And Sufficient

Using the topology T in a topological space (X,T), a new class of generalized open sets called ?-preopen sets, is introduced and studied. This class generates a new topology Tg which is larger than T? and smaller than T??. By means of the corresponding interior and closure operators, among other results, necessary and sufficient conditions are given for Tg to coincide with T? , T? or T??.

scholarly journals Supports of Borel measures

1979 ◽  
Vol 27 (2) ◽  
pp. 221-231 ◽  
Author(s):  
Susumu Okada
Keyword(s):  
Borel Measure ◽  
Topological Spaces ◽  
New Class ◽  
Borel Measures ◽  
Refinable Space

AbstractWe present a new class of topological spaces called SL-spaces, on which every Borel measure has a Lindelöf support. The class contains all metacompact spaces. However, a θ-refinable space is not necessarily an SL-space.

A View on Fuzzy Minimal Open Sets and Fuzzy Maximal Open Sets

2015 ◽  
Vol 7 (1) ◽  
pp. 62-73 ◽  
Author(s):  
Hamid Reza Moradi
Keyword(s):  
Topological Space ◽  
Topological Spaces ◽  
Basic Properties ◽  
New Class ◽  
Properties And Characterization ◽  
Open Set ◽  
Fuzzy Topological Space ◽  
Fuzzy Topological Spaces ◽  
Characterization Theorems

A nonzero fuzzy open set () of a fuzzy topological space is said to be fuzzy minimal open (resp. fuzzy maximal open) set if any fuzzy open set which is contained (resp. contains) in is either or itself (resp. either or itself). In this note, a new class of sets called fuzzy minimal open sets and fuzzy maximal open sets in fuzzy topological spaces are introduced and studied which are subclasses of open sets. Some basic properties and characterization theorems are also to be investigated.

scholarly journals On FuzzySp-Open Sets

2011 ◽  
Vol 2011 ◽  
pp. 1-5
Author(s):  
Hakeem A. Othman
Keyword(s):  
Topological Space ◽  
Continuous Mapping ◽  
Open Mapping ◽  
New Class ◽  
Fuzzy Topological Space ◽  
The Relationship

A new class of generalized fuzzy open sets in fuzzy topological space, called fuzzysp-open sets, are introduced, and their properties are studied and the relationship between this new concept and other weaker forms of fuzzy open sets we discussed. Moreover, we introduce the fuzzysp-continuous (resp., fuzzysp-open) mapping and other stronger forms ofsp-continuous (resp., fuzzysp-open) mapping and establish their various characteristic properties. Finally, we study the relationships between all these mappings and other weaker forms of fuzzy continuous mapping and introduce fuzzysp-connected. Counter examples are given to show the noncoincidence of these sets and mappings.

scholarly journals Contra-ω-Continuous and Almost Contra-ω-Continuous

2007 ◽  
Vol 2007 ◽  
pp. 1-13 ◽  
Author(s):  
Ahmad Al-Omari ◽  
Mohd Salmi Md Noorani
Keyword(s):  
Topological Space ◽  
Continuous Functions ◽  
New Class

The notion of contra continuous functions was introduced and investigated by Dontchev. In this paper, we apply the notion ofω-open sets in topological space to present and study a new class of called almost contraω-continuous functions as a new generalization of contra continuity.

scholarly journals Theory of g-Tg-Interior and g-Tg-Closure Operators: Definitions, Essential Properties, and Commutativity

2019 ◽  
Author(s):  
Mohammad Irshad KHODABOCUS ◽  
Noor-Ul-Hacq SOOKIA
Keyword(s):  
Topological Space ◽  
Topological Spaces ◽  
Closure Operators ◽  
New Class ◽  
Essential Properties ◽  
Generalized Topological Space ◽  
Outstanding Result

In a generalized topological space Tg = (Ω, Tg), ordinary interior and ordinary closure operators intg, clg : P (Ω) −→ P (Ω), respectively, are defined in terms of ordinary sets. In order to let these operators be as general and unified a manner as possible, and so to prove as many generalized forms of some of the most important theorems in generalized topological spaces as possible, thereby attaining desirable and interesting results, the present au- thors have defined the notions of generalized interior and generalized closure operators g-Intg, g-Clg : P (Ω) −→ P (Ω), respectively, in terms of a new class of generalized sets which they studied earlier and studied their essen- tial properties and commutativity. The outstanding result to which the study has led to is: g-Intg : P (Ω) −→ P (Ω) is finer (or, larger, stronger) than intg : P (Ω) −→ P (Ω) and g-Clg : P (Ω) −→ P (Ω) is coarser (or, smal ler, weaker) than clg : P (Ω) −→ P (Ω). The elements supporting this fact are reported therein as a source of inspiration for more generalized operations.

scholarly journals A Cartesian closed category of event structures with quotients

2006 ◽  
Vol Vol. 8 ◽  
Author(s):  
Samy Abbes
Keyword(s):  
Topological Space ◽  
Event Structure ◽  
Cartesian Closed Category ◽  
New Class ◽  
Closed Category ◽  
Event Structures ◽  
Natural Notion ◽  
International Audience ◽  
Cartesian Closed

International audience We introduce a new class of morphisms for event structures. The category obtained is cartesian closed, and a natural notion of quotient event structure is defined within it. We study in particular the topological space of maximal configurations of quotient event structures. We introduce the compression of event structures as an example of quotient: the compression of an event structure E is a minimal event structure with the same space of maximal configurations as E.

scholarly journals A Class of Separation Axioms in Generalized Topology

2016 ◽  
Vol 4 (2) ◽  
pp. 151-159
Author(s):  
D Anabalan ◽  
Santhi C
Keyword(s):  
Topological Space ◽  
Generalized Topology ◽  
Regular Space ◽  
Topological Spaces ◽  
Closed Sets ◽  
New Class ◽  
Separation Axioms ◽  
Generalized Topological Space

The purpose of this paper is to introduce and study some new class of definitions like µ-point closure and gµ –regular space concerning generalized topological space. We obtain some characterizations and several properties of such definitions. This paper takes some investigations on generalized topological spaces with gµ –closed sets and gµ–closed sets.

scholarly journals Attractors of iterated function systems and Markov operators

2003 ◽  
Vol 2003 (8) ◽  
pp. 479-502 ◽  
Author(s):  
Józef Myjak ◽  
Tomasz Szarek
Keyword(s):  
Iterated Function Systems ◽  
Markov Operators ◽  
New Class ◽  
Borel Measures ◽  
Transition Functions ◽  
Iterated Function ◽  
Banach Contraction ◽  
Complete Separable Metric Space ◽  
The Banach Contraction Principle ◽  
Separable Metric Space

This paper contains a review of results concerning “generalized” attractors for a large class of iterated function systems{wi:i∈I}acting on a complete separable metric space. This generalization, which originates in the Banach contraction principle, allows us to consider a new class of sets, which we call semi-attractors (or semifractals). These sets have many interesting properties. Moreover, we give some fixed-point results for Markov operators acting on the space of Borel measures, and we show some relations between semi-attractors and supports of invariant measures for such Markov operators. Finally, we also show some relations between multifunctions and transition functions appearing in the theory of Markov operators.

scholarly journals Fuzzy-interval inequalities for generalized convex fuzzy-interval-valued functions via fuzzy Riemann integrals

2021 ◽  
Vol 7 (1) ◽  
pp. 1507-1535
Author(s):  
Muhammad Bilal Khan ◽  
◽  
Hari Mohan Srivastava ◽  
Pshtiwan Othman Mohammed ◽  
Dumitru Baleanu ◽  
...  
Keyword(s):  
Optimization Problems ◽  
Fuzzy Optimization ◽  
Type Inequality ◽  
Discrete Form ◽  
Basic Properties ◽  
New Class ◽  
Riemann Integrals ◽  
Interval Valued ◽  
Fuzzy Interval

<abstract> <p>The objective of the authors is to introduce the new class of convex fuzzy-interval-valued functions (convex-FIVFs), which is known as $ p $-convex fuzzy-interval-valued functions ($ p $-convex-FIVFs). Some of the basic properties of the proposed fuzzy-interval-valued functions are also studied. With the help of $ p $-convex FIVFs, we have presented some Hermite-Hadamard type inequalities ($ H-H $ type inequalities), where the integrands are FIVFs. Moreover, we have also proved the Hermite-Hadamard-Fejér type inequality ($ H-H $ Fejér type inequality) for $ p $-convex-FIVFs. To prove the validity of main results, we have provided some useful examples. We have also established some discrete form of Jense's type inequality and Schur's type inequality for $ p $-convex-FIVFs. The outcomes of this paper are generalizations and refinements of different results which are proved in literature. These results and different approaches may open new direction for fuzzy optimization problems, modeling, and interval-valued functions.</p> </abstract>

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