Integral Inequalities and Generalized Convexity

Mishra, Shashi Kant, Sharma, Nidhi, Bisht, Jaya

Integral Inequalities and Generalized Convexity
  • 出版商: CRC
  • 出版日期: 2023-09-18
  • 售價: $4,130
  • 貴賓價: 9.5 折 $3,924
  • 語言: 英文
  • 頁數: 258
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 1032526327
  • ISBN-13: 9781032526324

    • 下單後立即進貨 (約2~4週)

商品描述

The book covers several new research findings in the area of generalized convexity and integral inequalities. Integral inequalities using various type of generalized convex functions are applicable in many branches of mathematics such as mathematical analysis, fractional calculus, and discrete fractional calculus.

The book contains integral inequalities of Hermite-Hadamard type, Hermite- Hadamard-Fejer type and majorization type for the generalized strongly convex functions. It presents Hermite-Hadamard type inequalities for functions defined on Time scales. Further, it provides the generalization and extensions of the concept of preinvexity for interval-valued functions and stochastic processes, and give Hermite-Hadamard type and Ostrowski type inequalities for these functions. These integral inequalities are utilized in numerous areas for the boundedness of generalized convex functions.

Features:

  • Covers Interval-valued calculus, Time scale calculus, Stochastic processes - all in one single book
  • Numerous examples to validate results
  • Provides an overview of the current state of integral inequalities and convexity for a much wider audience, including practitioners
  • Applications of some special means of real numbers are also discussed

The book is ideal for anyone teaching or attending courses in integral inequalities along with researchers in this area.

商品描述(中文翻譯)

這本書涵蓋了廣義凸性和積分不等式領域的幾項新研究發現。使用各種類型的廣義凸函數的積分不等式在數學的許多分支中都有應用，例如數學分析、分數微積分和離散分數微積分。

這本書包含了廣義強凸函數的Hermite-Hadamard型、Hermite-Hadamard-Fejer型和majorization型的積分不等式。它提出了定義在時間尺度上的函數的Hermite-Hadamard型不等式。此外，它還對區間值函數和隨機過程的preinvexity概念進行了推廣和擴展，並給出了這些函數的Hermite-Hadamard型和Ostrowski型不等式。這些積分不等式在許多領域中用於廣義凸函數的有界性。

特點：
- 包含區間值微積分、時間尺度微積分、隨機過程等內容，一本書涵蓋多個主題
- 大量的例子來驗證結果
- 為更廣泛的受眾提供積分不等式和凸性的現狀概述，包括從業人員
- 還討論了一些特殊實數平均值的應用

這本書非常適合教授或參加積分不等式課程的人，以及這個領域的研究人員。

作者簡介

Shashi Kant Mishra Ph.D., D.Sc. is Professor at the Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi, India, with over 24 years of teaching experience. He has authored eight books, including textbooks and monographs, and has been on the editorial boards of several important international journals. He has guest edited special issues of the Journal of Global Optimization; Optimization Letters (both Springer Nature) and Optimization (Taylor & Francis). He has received INSA Teacher Award 2020 from Indian National Science Academy, New Delhi and DST Fast Track Fellow 2001 from Ministry of Science and Technology, Government of India. Prof. Mishra has published over 203 research articles in reputed international journals and supervised 21 Ph.D. students. He has visited around 15 institutes/ universities in countries such as France, Canada, Italy, Spain, Japan, Taiwan, China, Singapore, Vietnam, and Kuwait. His current research interest includes mathematical programming with equilibrium, vanishing and switching constraints, invexity, multiobjective optimization, nonlinear programming, linear programming, variational inequalities, generalized convexity, integral inequalities, global optimization, nonsmooth analysis, convex optimization, nonlinear optimization, and numerical optimization.

Nidhi Sharma is Fellow of the Council of Scientific Industrial Research (CSIR) at the Department of Mathematics, Institute of Science, Varanasi, India. She received the M.Sc. degree in Mathematics from Banaras Hindu University, Varanasi, India. She is working on generalized convexity and integral inequalities under the supervision of Prof. S. K. Mishra. Her current research interests include integral inequalities, generalized convexities, set valued functions, and stochastic process.

Jaya Bisht is DST INSPIRE Fellow (Senior Research Fellow) at the Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi, India. She received BSc. and M.Sc. degree in Mathematics from Hemwati Nandan Bahuguna Garhwal University (Central University), Srinagar, India. She is awarded Junior Research Fellowship (JRF) from Human Resource Development Group of Council of Scientific Industrial Research (HRD-CSIR), Government of India. Her current research interest includes integral inequalities, generalized convexities, Set valued functions, and stochastic process.

作者簡介(中文翻譯)

Shashi Kant Mishra博士是印度瓦拉納西市Banaras Hindu大學科學學院數學系的教授，擁有超過24年的教學經驗。他撰寫了八本書籍，包括教科書和專著，並擔任多個重要國際期刊的編輯委員會成員。他曾擔任Springer Nature出版的《Journal of Global Optimization》和《Optimization Letters》以及Taylor & Francis出版的《Optimization》的特刊編輯。他曾獲得印度國家科學院（Indian National Science Academy）頒發的2020年INSA教師獎和印度科學與技術部（Ministry of Science and Technology, Government of India）頒發的2001年DST Fast Track Fellow獎。Mishra教授在知名國際期刊上發表了203篇研究論文，並指導了21名博士生。他曾訪問過法國、加拿大、意大利、西班牙、日本、台灣、中國、新加坡、越南和科威特等15個國家的大約15所研究機構/大學。他目前的研究興趣包括具有均衡、消失和切換約束的數學規劃、非線性規劃、線性規劃、變分不等式、廣義凸性、積分不等式、全局優化、非光滑分析、凸優化、非線性優化和數值優化。

Nidhi Sharma是印度瓦拉納西市Banaras Hindu大學科學學院數學系的科學工業研究委員會（CSIR）研究員。她在印度瓦拉納西市Banaras Hindu大學獲得數學碩士學位。她在Mishra教授的指導下從事廣義凸性和積分不等式的研究。她目前的研究興趣包括積分不等式、廣義凸性、集合值函數和隨機過程。

Jaya Bisht是印度瓦拉納西市Banaras Hindu大學科學學院數學系的DST INSPIRE研究員（高級研究員）。她在印度Hemwati Nandan Bahuguna Garhwal大學（中央大學）獲得數學學士和碩士學位。她獲得了印度科學工業研究委員會（HRD-CSIR）人力資源發展組頒發的初級研究員（JRF）獎。她目前的研究興趣包括積分不等式、廣義凸性、集合值函數和隨機過程。

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