$w^*$-$w^*$-continuous
در نشریات گروه ریاضی-
In this paper, we consider a general class of nonautonomous abstract delayed evolution equations with a nonlinear source term. Under appropriate assumptions on the time-independent operator and the initial data, we establish global existence using the method of steps and employing classical results from the theory of inhomogeneous evolution problems. Then, by assuming that the operator associated with the non-delayed part of the system generates an exponentially stable semigroup, we obtain an exponential decay estimate. This is achieved through a direct proof based on Duhamel's formula combined with Gronwall's inequality, under Lipschitz continuity conditions on the nonlinear source term. Finally, we conclude the paper by providing illustrative examples that validate the generalized setting of our system.Keywords: Duhamel's Formula, Energy Function, Evolutionary Family, Lipschitz Continuous
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International Journal Of Nonlinear Analysis And Applications, Volume:14 Issue: 1, Jan 2023, PP 1 -10In the present paper, we prove common fixed point theorem for F-contraction by considering one map is orbitally continuous map in $\Omega-$Extended rectangular b-metric space. In addition, we find fixed point for Banach and Kannan type contraction inequality without consideration of orbitally continuity. Also at the fixed point maps does not force to be continuous. An examples is also provided for the utility of our results.Keywords: Extended rectangular b-metric space, F-contraction, Orbitally continuous, Common fixed point, Fixed point
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Thangaraj and Balasubramanian introduced the so-called somewhat fuzzy semicontinuous and somewhat fuzzy semiopen functions. Two years later, the same authors defined two other types of functions called somewhat fuzzy continuous and somewhat fuzzy open without indicating connections between them. At first glance, we may easily conclude (from their definitions) that every somewhat fuzzy continuous (resp. open) function is slightly fuzzy semicontinuous (resp. semiopen) but not conversely. In this note, we show that they are equivalent. We further prove that somewhat fuzzy continuous functions are weaker than fuzzy semicontinuous functions.Keywords: fuzzy continuous, somewhat continuous, somewhat fuzzy continuous, somewhat fuzzy semicontinuous, somewhat fuzzy open
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International Journal Of Nonlinear Analysis And Applications, Volume:13 Issue: 2, Summer-Autumn 2022, PP 3115 -3126
In this research, we prove the results of n-tuple fixed point in partially ordered cone metric spaces. We will impose some conditions upon a self-mapping and a sequence of mappings via α-series. This series are wider than the convergent series. Also, at the end of this paper, an example is provided to illustrate the results.
Keywords: alpha-series, n-tuple fixed point, n-tuple coincidence point, cone metric space, compatible mappings, reciprocally continuous -
The aim of this paper is to introduce the concepts of $alpha$-continuity, $eta$-admissible pair for fuzzy set-valued maps and define a notion of fuzzy $eta-(psi, F)$-contraction. The existence of common fuzzy fixed points for such contraction is investigated in the setting of a complete metric space. The ideas presented herein complement the results of Wardowski, Banach, Heilpern and other results on point-to-point and point-to-set-valued mappings in the comparable literature of metric and fuzzy fixed point theory. A few important of these consequences of our results are highlighted and discussed. Some nontrivial examples and an application to a system of integral inclusions of Fredholm type are considered to support our theorems and to illustrate a usability of the results obtained herein.
Keywords: fuzzy set, fuzzy fixed point, F-contraction, α-continuous, η-admissible, fuzzy η − (ψ, F)-contraction, integral inclusion -
Weighted integral inequalities for general integral operators on monotone positive functions with parameters $p$ and $q$ are established in [4]. The aim of this work is to extend the results to different cases of these parameters, in particular for negative $p$ and $q$. We give some new lemmas which will be frequently used in the proofs of the main theorems.Keywords: General integral operator, Weighted inequalities, Monotone functions, Absolutely continuous
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International Journal Of Nonlinear Analysis And Applications, Volume:12 Issue: 1, Winter-Spring 2021, PP 1251 -1260
In this paper, the concept of $etaxi$-monotonous operator is explored using KKM mapping. The existence results and uniqueness dened on its bounded and unbounded domains are discussed. Our ndings improve and develop some well-known solutions in literature.
Keywords: Monotonicity, Equilibrium problem set-valued mapping, Hemicoutinuity, KKM-mapping, Semi continuous, Convex function -
در این مقاله مفاهیم پیوسته مداری و تام مداری روی فضای متریک -C* جبر-مقدار تعریف می کنیم. اگر T یک نگاشت پیوسته مداری روی فضای متریک -C* جبر-مقدار (X,A,d) که X یک مجموعه ی ناتهی، 𝔸 یک −𝐶∗ جبر یکانی با رابطه ی ترتیب جزیی طبیعی ⪯ باشد ، نشان می دهیم که تحت شرایطی برای هر x∈X دنباله کوشی به فرم {Tn (x)} به یک نقطه ثابت T همگرا است. سپس ثابت می کنیم که تحت چه شرایطی یک نگاشت پیوسته مداری روی یک فضای متریک -C* جبر-مقدار (X,A,d) دارای نقطه تناوبی است. همچنین نشان می دهیم که تحت چه شرایطی یک خود- نگاشت پیوسته مداری روی یک فضای -b متریک -C* جبر-مقدار (X,A,d) دارای حداقل یک نقطه ثابت است. علاوه بر این اثبات می کنیم اگر T یک خود-نگاشت مداری روی فضای متریک -C* جبر-مقدار کامل (X,A,d) و نقطه x0∈X وجود داشته باشد به طوری که T2 (x0)≠x 0و T برخی شرایط دیگری نیز داشته باشد، آنگاه T دارای نقطه ثابت است.کلید واژگان: نقطه ثابت، - پیوسته مداری، نقطه تناوبی، فضای -bمتریک - C*جبر-مقداIn this paper, we first define the notions of orbitally continuous and orbitally complete on a C*-algebra-valued metric space. We show that if T is an orbitally continuous mapping on a C*-algebra-valued metric space (X,A, d), where X is a nonempty set and A is a C*-algebra with the relation ⪯ and if T orbitally complete and satisfies some conditions, then for any x∈X the iterated sequence {Tn (x)} converges to a fixed point of T. Also, we prove that an orbitally continuous mapping on a C*-algebra-valued metric space (X,A, d) under conditions has a periodic point. It is prove that an orbitally continuous self-map on a C*-algebra-valued b-metric space (X,A, d) under which conditions has at least a fixed point. In additions, if (X,A, d) be a complete C*-algebra-valued metric space and T has some property. Then T has a fixed point in X provided that there exists x0∈X such that T2 (x0)≠xKeywords: fixed point, orbital continuous, periodic point, C*-algebra -valued b-metric spaces
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In this paper, we define a new concept of factorization for a bounded bilinear mapping $f:Xtimes Yto Z$, depended on a natural number $n$ and a cardinal number $kappa$; which is called $n$-factorization property of level $kappa$. Then we study the relation between $n$-factorization property of level $kappa$ for $X^*$ with respect to $f$ and automatically boundedness and $w^*$-$w^*$-continuity and also strong Arens irregularity. These results may help us to prove some previous problems related to strong Arens irregularity more easier than old. These include some results proved by Neufang in ~cite{neu1} and ~cite{neu}. Some applications to certain bilinear mappings on convolution algebras, on a locally compact group, are also included. Finally, some solutions related to the Ghahramani-Lau conjecture is raised.Keywords: Bilinear map, Factorization property, Strongly Arens irregular, Automatically bounded, $w^*$-$w^*$-continuous
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In this paper, the concept of somewhat-connected space will be introduced and characterized. Its connection with the other well-known concepts such as the classical connectedness, the $omega_theta$-connectedness, and the $omega$-connectedness will be determined. Moreover, the concept of textit{somewhat}-continuous function from an arbitrary topological space into the product space will be characterized.Keywords: Somewhat-open, somewhat-closed, somewhat-connected, somewhat-continuous
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The main goal of the present paper is to extend classical results from the measure theory and dynamical systems to the fuzzy subset setting. In this paper, the notion of dynamic equivalence relation is introduced and then it is proved that this relation is an equivalence relation. Also, a new metric on the collection of all equivalence classes is introduced and it is proved that this metric is complete.Keywords: Fuzzy measure algebra, Dynamical system, Equivalence relation, Uniformly continuous
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In this paper, we introduce the concept of rarely generalized regular fuzzy continuous functions in the sense of A.P. Sostak's and Ramadan is introduced. Some interesting properties and characterizations of them are investigated. Also, some applications to fuzzy compact spaces are established.Keywords: Rarely generalized regular fuzzy continuous, Grf, compact space, Rarely grf, almost compact space, Rarely grf, T2, spaces
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در این مقاله، هدف ما رده بندی پاسخ هایی است که به صورت آمیخته ای از پاسخ های گسسته و پیوسته هستند. برای این کار، ابتدا باید تابع توزیع توام چنین پاسخ هایی را داشته باشیم. بنابراین، مدل مکانی عام جدید را برای دستیابی به تابع توزیع توام پاسخ های آمیخته ی گسسته و پیوسته معرفی کرده ایم و به صورت اجمالی با مدل مکانی عام د لئون و کریر [1] مورد مقایسه قرار داده ایم. رویکرد مورد استفاده برای رده بندی چنین پاسخ هایی، استفاده از قاعده ی رده بندی ولچ [2] به همراه ارائه ی احتمال های بد-رده بندی و نرخ واقعی خطا برای این مدل است. همچنین نتایج رده بندی مدل مکانی عام جدید با نتایج رده بندی مدل مکانی عام مورد مقایسه قرار گرفته است [1]. لازم به ذکر است قواعد رده بندی نمونه ای برای مدل مکانی عام جدید با استفاده از برآوردهای به دست آمده از طریق ماکسیمم سازی تابع درستنمایی مطرح می شود. در پایان، برای نشان دادن قابلیت قواعد به دست آمده، مطالعه ی شبیه سازی و تحلیل داده های واقعی با استفاده از مدل مکانی عام جدید انجام شده است.
کلید واژگان: قواعد رده بندی، مدل مکانی عام، پاسخ های آمیخته ی پیوسته و گسسته، تابع درستنمایی، احتمال بد، رده بندیIn this paper، Our goal is classifying the responses which are mixed discrete and continuous responses. So، first we are modeling them then get their classification rules using the Welch’s classification rules (1939) along with their misclassification probabilities.. Also، sample classification rules are reached using the MLE. Finally، simulation study and some real data are analyzed have performed to show the performance of the rules.Keywords: Classification rule, General location model, Continuous, Discrete mixed data, Likelihood Function, Misclassification Probability -
In this paper we present some properties of set-norm exhaustive set multifunctions and also of atoms and pseudo-atoms of set multifunctions taking values in the family of non-empty subsets of a commutative semigroup with unity.Keywords: Set, norm, Exhaustive, Continuous, Null, null, additive, Atom, Pseudo, atom
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