Báo cáo hóa học: " Research Article Generalizations of Shafer-Fink-Type Inequalities for the Arc Sine Function"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Generalizations of Shafer-Fink-Type Inequalities for the Arc Sine Function | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2009 Article ID 705317 6 pages doi 2009 705317 Research Article Generalizations of Shafer-Fink-Type Inequalities for the Arc Sine Function Wenhai Pan and Ling Zhu Department of Mathematics Zhejiang Gongshang University Hangzhou Zhejiang 310018 China Correspondence should be addressed to Ling Zhu zhuling0571@ Received 29 December 2008 Revised 9 March 2009 Accepted 28 April 2009 Recommended by Sever Dragomir We give some generalizations of Shafer-Fink inequalities and prove these inequalities by using a basic differential method and l Hospital s rule for monotonicity. Copyright 2009 W. Pan and L. Zhu. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. Introduction Shafer see Mitrinovic and Vasic 1 page 247 gives us a result as follows. Theorem . Let x 0. Then 6 V1 x - V1 - xi 3x arcsinx 4 VTĨĨ A 2 . The theorem is generalized by Fink 2 as follows. Theorem . Let 0 x 1. Then x . . nx --- arcsinx - 2. Furthermore 3 and n are the best constants in . In 3 Zhu presents an upper bound for arcsin x and proves the following result. 2 Journal of Inequalities and Applications Theorem . Let 0 x 1. Then 3x 6 V1 x V1 x ----- ----------- ------ arcsinx 2 v1 x2 4 V 1 x v1 x _ _ __ n V2 1 2 V1 x V1 x nx 4 V1 x V1 x 2 V1 x2 Furthermore 3 and n 6 and n V2 1 2 are the best constants in . Malesevic 4-6 obtains the following inequality by using l-method and computer separately. Theorem . Let 0 x 1. Then arcsinx n 2 V Y x 2V2 fvrrx VT x _ _ _2 r _ _ _ __ _ __ _ __ 14 V2 4 n n 2V2 V1 x V1 x _ 2 n 2 V1 X2 Zhu 7 8 offers some new simple proofs of inequality by L Hospital s rule for monotonicity. In this paper we give some generalizations of these above results and obtain two new

Không thể tạo bản xem trước, hãy bấm tải xuống
TÀI LIỆU LIÊN QUAN
TÀI LIỆU MỚI ĐĂNG
203    21    1    07-07-2022
56    13    1    07-07-2022
30    14    1    07-07-2022
92    17    1    07-07-2022
Đã phát hiện trình chặn quảng cáo AdBlock
Trang web này phụ thuộc vào doanh thu từ số lần hiển thị quảng cáo để tồn tại. Vui lòng tắt trình chặn quảng cáo của bạn hoặc tạm dừng tính năng chặn quảng cáo cho trang web này.